FYI, TS member Heath is a professional transfer expert, perhaps he'll drop in here.
Regardless of whether it occured in the recorder or playback machine, if the pitch variance is constant and was caused by tape speed being off for whatever reason, then pitch and tempo should be adjusted together and the relationship between the two should remain locked. This is normal tape behaviour people will be familiar with- faster playback increases pitch and tempo and shortens playback time, slowing playback tape speed does the opposite. Lets assume that's the case.
A different scenario would be if all the instruments were mis-tuned (yet are in tune with each other) and that is what one wishes to correct. In that case one might not worry too much about the small change in tempo and run time want to adjust pitch while not changing tempo or runtime, in order to retain sync with video for example. This requires a more advanced tool, yet is available in many editors these days. Key words may be pitch-adjust, elastic-audio, etc.
First challenge is determining if the pitch/tempo is indeed incorrect.
Second is determining if it should be corrected or if it can be left alone.
Third is making the correction, if that is deemed appropriate.
How might one determine if it is incorrect?
Compare run time against alternate sources (marking identical start and end points)
Compare pitch against alternate sources (by ear, switching back and forth rapidly)
Determining if it needs to be be corrected may well be entirely subjective.
If using a varispeed tape machine for doing the transfer, the tape speed (and thus pitch) can be adjusted upon playback prior to digitalization. Otherwise, how specifically to make the correction will likely depend on the editing software you are using. Let us know that and folks using the same software can comment from experience. The "old school way" is to do a calculation, manually resample to a slightly higher or lower sample rate, and then playback the file at the standard rate.