Well, as long as they don't interfere too much, I 
guess leaving the tape where it is would be the 
best decision.  Although they might cause 
chemical problems as they age and deteriorate, 
the trade-off would be risking damaging the 
original paints on the backgrounds and/or cels by 
attempting to remove the tape.

Cut-outs are not too unusual (I may have come 
across them once or twice) and most likely it was 
part of the production.  The only sure way to 
tell is to the identify and view the scene from 
the actual anime, though.  To me, however, it 
would be baffling for anyone outside the 
production to spend their time taping nice little 
tree cut-outs to backgrounds (unless a previous 
owner of the cels were letting their kids play 
around with them, which seems unlikely).

Never came across a photo background before, but 
directors might try different things to achieve a 
certain effect (again, the best thing to do is 
actually check the anime).  Unusual, but not of 
the question.  For example, laser-copy 
backgrounds were pretty much non-existant up 
until about 5 or so years ago.