One option is to stop using the garlic press. This is a tool that results in the waste that you describe, plus it takes time to clean after use. Instead, just use a knife. With a chef's knife, for example, you can slice, chop, mince, or crush (more options than a garlic press!). The advantages are many. First, you can prep your garlic in a variety of ways. The flavor and aroma garlic adds to a dish can be greatly controlled by how it is prepared. Then, you only have the peel to dispose of, and the knife can simply be washed off.

Personally, I use a small extra container with a well-closing lid and a handle for food waste like fruit and vegetable peels, meat chunks I don't want to eat, etc., about 7 litres of volume. Because this small container becomes full quite fast, I have to regularly empty it into the big bin (biological waste goes into a separate container where I live) outside my house. Something like this:

This reduces the amount of smell that can develop, plus the lid usually stops pests like fruit flies from multiplying (not 100%, but it helps). After emptying this container, I wash it out with hot water and a bit of dish soap to get rid of smells and sticky chunks. This remainder goes down the drain easily. You could also line this bucket with a biodegradable plastic bag if your municipality does not have big bins for biological waste or you get rid of your waste differently.

This may not be practical for dishes where the garlic is not cooked (e.g. salad dressings) but at least while cooking I typically just add the remnant to the food along with the pressed garlic, so there is no need to dispose it.

As mentioned in the comments, you can also chop up the remnants with a knife if the parts are too big for your taste

I've never used one myself (I normally just chop or squash garlic with a knife), but how about a garlic rocker?

You can use all of the garlic without having to spend ages extracting it from the press. Cleanup is easier too.

I guess it's likely that you'll have left-over garlic too. Just stick it in tupperware in the fridge and use it in your next meal.

Or sprinkle it onto your window-frames to ward off 'creatures of the night'!

Put the remnants in an old jar in the freezer until its time to dispose of it. The reduced "vapour pressure" from freezing the pungent remnants (reducing oil vapour pressure) will reduce smells drastically, as will the sealing action of the jar. You might be able to get away with just using the fridge, or even just the jar...

This sort of thing was one reason I switched to using a small bin in the kitchen. Not just garlic and onion scraps, but blue cheese packaging, which is probably even worse. Now I have the same issue with the food waste (composting) bin, which fills up more slowly.

You have a few options.

• The first is to scrape out the garlic press into something other than the kitchen bin, like some non-recyclable packaging from preparing the same meal, and take that promptly directly to the outside bin. That only helps if there is one and it's not too far, not so convenient in many apartments.
• Similarly, you could just take out the kitchen bin half full, perhaps gathering other rubbish into it first from the rest of the home.
• The third option is to make good use of any non-recyclable packaging again, ideally a plastic bag without holes, and use that to contain the garlic within the bin, knotting it. Even a plastic bag with holes is of some benefit.
• Washing the scraped out crushed garlic away down the sink will deal with that, but not any larger trimmings unless you have a waste disposal unit.
• Even my dishwasher helps with the smell, but it's not good at removing the crushed garlic in the first place (a washing up brush or butter knife is, then put that in the dishwasher too).
• I usually scrape most of the left-behind crushed garlic into the pan anyway

Put the garlic remains, along with onion skins, carrot tops, celery bottoms, broccoli stems, and other vegetable waste in a plastic bag or other container in the freezer. When full, put it in a crock pot, fill with water, and make vegetable stock.

Can you install a garbage disposal? This is a mincer/grinder that is inline in the sink's drain. Food remains gets flushed down the sink without clogging.

But you probably do have another device that already can handle large chunks of solid waste and sends them to the sewer. When my in-laws were visiting from China, I saw them empty the spent tea leaves from the teapot into the toilet. The same thing would work for any chopped veggie bits.

update

To clarify, tea leaves and minced garlic are examples which are well minced, not large hard items or unbroken peels that can act like ribbons, etc.

I have a reused icecream tub in the freezer. Anything potentially stinky goes in there and freezes till bin-day. We just empty that into the organics bin in the morning, and it stays frozen for hours until the truck comes.

Works fine for bones, chicken skin, etc that can't be composted but can be disposed in the organics waste stream (area dependent of course)

Some anti-smell cat litter in the bottom of your general 'waste intended for compost' bin..dig down to it when disposing of smelly items and bury it. If you are having to dig too far, empty more frequently.

When it comes time to get it out, just sift like normal cat box disposal after moving the top layers to the compost heap.

I would not suggest 'normal' soil as it can have eggs waiting to hatch.

If you have a yard then toss it in the grass.

Assuming you're not throwing away pounds of this stuff then it will be eaten/decomposed within mere days.

I always huck my kids' goldfish (crackers), cookies, and candy into my yard and I'd be hard-pressed to say I see a single trace after 3 days.

Small zip-lock style bags are ideal for this purpose. You can get a box of 90 for roughly $2.00 and they are good for any number of things, (including diapers, if your family is at that stage).

The best thing to do as someone mentioned earlier is to throw it in a stockpot but only if used to cook for self. Otherwise throw it in the compost heap. With regard to the fibrous tissue that remains you can scrape it out with a fork and compost it. If you want to mince then crush to make paste it’s best to sprinkle some coarse salt on it and its much quicker and one less thing to clean up. To clean your hands, wash with soap and water while rubbing your hands on some. It really does work on your hand

Where I live rubbish is separated, so plastic bags etc are out of the question.

We have 4 bins in the kitchen; one is for compost and one for other biological waste. To keep down the smell and to discourage the damned fruit flies, we wrap wet or smelly waste in newspaper or similar.

Newspaper composts down nicely in small amounts. If you are a composter you need to be sure that your newspaper is not poisonous.