Damaged sheetrock should always be replaced as a rule. It's not really harmful to tile a kitchen splash over some sheetrock mud, but if there's a lot of repair I'd replace it. Large areas of sheetrock mud should generally be primed, (not
finish painted), before tiling.
If you replace areas of sheetrock, fill and tape the joints with sheetrock mud and paper tape. Much stronger joints than the mesh stuff.
My opinion; worth price charged.