I have a large collection of paper tapes that came
with a
vintage Altair 680b and Teletype model 33 that I
inherited. I've restored the machines and have started
looking at the tapes. Unfortunately, I have discovered
that the rubber bands that were used to keep the tapes
rolled up have all dissolved into a yucky gooey mess that
is in most cases, stuck to the tapes.
I don't have experience with paper tape. From the
description it sounds like the oils dissolved the rubber by
acting as a solvent to the natural oils in rubber. If this
is the case, you could try something that can act as a
solvent to the oils, such as acetone.
You'll have to test against a sample tape, and don't assume
that the acetone or other solvent wont remain in the tape
and cause damage in the future. You should try to find a way
to copy new paper tapes or transfer the data to some other
medium.
How much data is in the exposed tape that was damaged? Don't
they have leaders with no data on them? Did the damage
extend into the layers beneath the surface? I'm assuming
that the tapes were rolled up and only the first few inches
were damaged.