The really correct way to clean these is with what is called a “dry sponge” or “dry cleaning sponge” you can get these from cleaning supply companies. They are also not difficult to find online (you can search under dry cleaning sponge). These are not regular sponges, but chemically treated sponges that are used for cleaning oil paintings among other things.
A simple home remedy for this is to use white bread (like wonder bread from the grocery store). You can scrunch this up like a sponge, and blot the batik painting or oil painting clean this way. Even though this felt a little weird to do, I have done this myself with an oil painting and it worked great.