Using a strainer is highly recommend in not only your kitchen sink but also all drains. Letting large particles into the drain can cause a blockage which could cause not only issues in your unit, but also neighbouring units even floors below you.
Do not let large particles go down your sink!
If you would like to dispose of grease, fat, or any other fluids that congeal at room temperature, seal in a jar or zip lock plastic bag and throw out with the garbage. Bacon fat can be refrigerated in the jar until it hardens for disposal.