After you've removed the tile, cut or scrape any hanging bits of paper off. Then paint the paper and any exposed areas of drywall core with PVA primer. Then you can use thinset. Although for backsplashes I prefer to use mastic, you can apply it with an 1/8" V groove trowel and avoid it pushing through the grout lines on the mosaic tiles. Also the OmniGrip brand is very sticky and so holds the individual small tiles better than thinset.