How would you repair this exterior foundation insulation/wrap?
It looks like EIFS, Exterior Insulation Finish System, placed over a pink sheet of fiberglass foundation drain board. EIFS is not made to go at or below grade. I am not a pro of this material, but I have never seen it applied over a fiberglass sheet. There was a post I answered sometime back, about how to repair EIFS that I did not format properly and still don't know how to, (moderators got on me about it) but if you do a search on EIFS and it's repair, it will tell you all about it.

In my opinion, this stuff should not be on there. it goes to grade and the fiberglass is a freeway for termites and other pests to get to your framing.

If you remove it and find an unsuitable surface under it, you can fasten a galvanized expanded metal lathe over the exposed surfaces and have 2 coats of type "S" masonry cement troweled over it. First coat is a scratch coat, the second is a finsh coat. EIFS can even be troweled on over all this as a finish too, but don't run it to grade, leave it a few inches up. It may not need wire lathe over it if the surface is clean masonry or cement, but I figure it has some type of bonding agent or waterproofing to get the fiberglass to stick to it before the EIFS went on...