If you are using an unidirectional condenser mic with a cardiod pattern very close to the guitar and the tone is in the low range, you might be experiencing a proximity effect. Two things to try:
1. Use an omnidirectional mic in the same room. You may pick up some other sounds, but see if it clears up the overtone. If so, then it is the proximity effect.
2. If that works, two solutions are to try moving the mic or using a mic other than a condenser. Something like a ribbon mic or an SM57 might be worth a try.
Good luck.