IMO it's very unlikely, however it is possible. The stay cap is mostly cosmetic, and the exposed seam all looks good. That's why I wouldn't be to concerned about filing the blobs flush. The blob that connects the stay to the frame is structural. Don't attack that one too much, but you want to see a crack there if there is one. I bet it's fine though.

Anyhow, "digging" should be avoided. A single cut flat file with no handle is what I'd suggest, using the stay as a guide to keep it flush. You could put a couple layers of tape on the lower half of the file. That way the file won't quite touch the steel.