What type of back-splash?

Thank you for responding, Brickeyee. The proposed backsplash is 1X1 tiles on a net backing. The brown paper wallboard left exposed after removing the old 4x4 tiles is a little rough in spots but has no gouges or holes. Thought I should inquire whether applying some sort of treatment is recommended, instead of just slapping on the thinset.

A kitchen back-splash is not a wet enough location to require cement backer board, though it can always be used.

A coat of primer to limit moisture movement into the base from the thin set would be a good idea.

If the thin set dries out before curing it will have greatly reduced strength, and wallbooard loves to absorb moisture.

Thank you very much for the explanation! My vague and unspecified anxiety about omitting an important step is now allayed.

Sand the rough stuff so it's flush/flat with the rest (any small voids that remain are ok). Then prime as mentioned.

If you happen to be using glass tiles, you can find a glass nipper (it has opposing cutting wheels) at a craft store. For some reason most tile supplies still don't carry that type of nipper.

One final bit of advice: consider your starting point carefully to limit the edge cuts elsewhere, like around outlets, edges of cabinets, etc.