You're right. Avoid putting grease and cooking oil down the kitchen sink. Some people think it is okay to put them down the toilet, but that's bad too. The grease can clog pipes in your own apartment or house. The fats can also cause problems down the line as they continue through the system.
If there is a small amount of fat, you can let it cool in the pan. When it hardens, wipe it into the garbage using a paper towel. For larger amounts, pour it into a coffee can. Store the coffee can in the fridge or freezer and re-use it the next time there is more oil or grease to dispose of. These coffee cans should be carefully discarded in the household garbage.
Grease and cooking oil should not be added to compost, says The Backyard Gardener. They could attract animals and create smells.
Thanks for your question,