Can surgery to remove a ganglion on my hand (extensor ) damage your tendon sheath?

Can be removed: Yes it can be removed with out injuring tenon sheath.

Yes and no: Often the tendon sheath need to be opened slightly, especially for the small gangglions TAH appear in the dorsal part of the rwrist near the radiocarpal joint near the distal edge or the extensor retinaculum, in fact if the tendon sheatht or retinaculum os not opened there the ganglion can be missed....And typically it is not repaired.So yes it is "damaged" but not in the sense of the word.