You need to heat the scuff sheet up to remove it without taking half of the face with it. Ideally with a heart gun, but any heat source will work (hairdryer for example). Ensure you pull the sheet across the face gently from edge to edge, rather than toe to splice. Otherwise you'll again take some wood with you. Then heat up any residue and gently scrape this off.
Depending on the state of the bat you'll need wood glue, superglue, clamps and ideally an orbital sander. But if not you could hand sand it, but this will obviously take longer.
In terms of grits, this depends on what state the bats in. If it's old and knackered you could start with a coarse grit to take a decent amount off quickly, then work up. If it's just a light refurb then 120, 180, 240 should be fine. I go up a bit higher, but it's personal preference to get the finish you're happy with