I recommend Etude Lip & Eye Remover.

You need to use a makeup remover for eye makeup products like mascara and eyeshadow because foam cleanser alone can't remove them, and I recommend the Etude one. First of all, it is very affordable. I remember buying two for around 6-7,000 won during a sale. It's probably under 10,000 won!! Even though it's cheap, it removes makeup well, gently, and without irritation! Sometimes, some removers don't come off mascara well, but this one does! I'm currently using one, so I took a picture of the new one I have in storage.