To elaborate more, my mom had in her room at work a set of pictures/painting done on beaverboard (one side is plain, the other has a texture, picture is on textured side), frame is made from wood slats. Due to decades of dust gathering etc the background of the pictures turned from kinda ecru color to something brown-ish. I tried to use water or water with soap on back side but the effects were not good. It's not covered in varnish to protect the painting. These are and were not expensive but it's matter more of a sentiment.

Is there any way of cleaning such painting?

I don't know if its good reddit for such question, but since so many people here are painters then maybe apart of creating art, they have idea how to repair one :)