As previously reported, I'm helping a friend rebuild her International, her childhood bike.

The upper race was very difficult to remove. After I got it off, I saw why, but it's a bit mysterious. There's about 1/4 inch of good threads, then 1/4 inch of what looks like the result of cross-threading or forcing something with the wrong pitch (could that be the case with the headset that was on there?--the race and locknut are both marked 24 tpi).

When I got the race off, I did check the threads inside and there did not seem to be any shavings from either part.

I'm worried about re-installing the headset. This bike only has one fork, and I'm afraid of stripping off the remaining threads so that the headset won't hold together.

Would you chase the threads with a die (and what's the pitch?), or might that just remove precious material which was at least functional that last time the headset was on there?