Are you going to just replace the quarter round? If so, you need to scrape the excess paint off the wall. A razor scraper use vertically will do that. There will probably be damage to the paint above the excess paint line. If that line is just over the ridged line, shoe molding might work. Shoe molding is similar to quarter round but wider on one side.

If the damage is higher than what shoe would cover, the fix is custom trim, at least with the thickness. That means special tools(normal for many woodworkers, but not for DIYers) like jointers, planers, and shapers/router tables are needed. Tools your dad may have had and stuff his woodworking friends may have.

Thank you HandyMac. The damage is higher than what shoe would cover...and I'd prefer not to use it. But i actually don't even know how I would use it b/c it seems like the trim would need to be shaped under to go over the "notch" build into the stair skirt. If you have thoughts on that (or even just confirming that would need to be done), I would certainly appreciate it.

Difficult to see in the picture, but is the top outside edge of the trim higher than the part against the wall? And rounded?

If so, you will need to make trim the width of the flat part of the existing trim, so the trim sets in that area. There is not much point in trying to machine a matching surface.