<font color="blue"> Any tips on how to repair or fix? </font color>

This depends on how "critical" you are going to be when you judge the repair.

Ideally, you would find a piece of veneer somewhere else on the cabinet that you could remove, and where it would not show as much. That would match the best.

Or, you could try to purchase some veneer that would stain close to that.

If you replace the veneer or no, you have some glueing to do, anyway, to the remaining veneer, where it is popped up. Plain old Elmer's white glue (school glue) works just fine for this, as do many other types of glue. You'll want to put pressure on it, and use a block of wood between the pressure and the work to spread out the force, and a piece of wax paper in there, too, to keep any squeezed out glue from sticking to the pressure block or clamp.

For a cheapo fix, you could glue down the existing veneer that is popped up, and simply stain the wood where the veneer is missing.