Hi,
I found this in with a bunch of parts, so how can I remove the tape from this tiny spring without messing it up?

It's only on a small portion of the spring, but...

Turn it over so the tape is on top. Then put it on a soft surface, styrofoam would maybe work. Balsa would work best. Lay a flat tothpick across the spring next to and parallel with the tape.

Hold the toothpick against the styrofoam on both sides of the hairspring to pin the Hairspring down to the styrofoam.

Slowly and Gently peel the tape off with a small tweezer. It should release from the restrained spring fairly easily.

A solvent, like alcohol or nail polish remover, might more safely dissolve the adhesive on the tape. Neither should hurt the hairspring and collet.

*** amended to note: actually, nail polish remover today is not pure acetone, but contains other chemicals and oils to protect your skin and make it more pleasant smelling, and may not be good for the hairspring.

Taking that course, the naptha component used and named as Zippo Lighter fluid will dissolve the adhesive, but I fear that it can leave a mess behind unless you soak it a lot.

Sheila,

I'm with Jerry and David here, I'd use a solvent like lighter fuel.
Drop a small amount on the spring/paper, let it soak for a few seconds, then hold the paper up so the spring can slide off under its own weight.

Once the spring is off, keep soaking until the goop is removed.
Beware that evaporation of the solvent can cause rust to form on the spring from any moisture in the atmosphere, but a drop of light watch oil should help protect it when you're done!

I'd avoid attempting to pick it off with anything.

John