How to take the solder off the thread?

OH,

I think you could simply run the nut in and it will cut through the solder. If that doesn't work, try some solder wick. It is a woven mesh of metal wire that will suck molten solder off of a solid surface.

I'm no expert, but for me, I press the hot solder iron against the solder wick, then against to solder on the sufrace you wish to remove it from. So, the solder wick will heat up, transfer the heat to the solder and suck it off.

Enjoy,

TIC

I beleive Reubent has nailed this one.

A wire brush may work if you can heat up the solder.
..or can you cut new threads with a tap & die?

Don't use a nut.
Use the appropriate die.
A die is made to cut plus it has an area for the removed material to collect.