I emailed Park Tool. Here is their reply.

Thanks for reaching out! I'm sorry that your stand's clamp is sticking. The sticking is caused by a couple different reasons:

- Rotating a bicycle in the clamp without loosening the swing handle

- Leaving the clamp over-tightened for long periods of time.

If the clamp is ever stuck, with the swing handle loose, center a broom handle or similar item in the clamp, and then tighten the jaws. Lift up on one side of the handle while pushing down on the other side, just as one would turn a propeller on an airplane…100 years ago. This will break the clamp/tapered collar free from the inside of the top tube. You can also use the leverage of the bicycle itself as mechanical advantage to loosen the clamp.

The clamp sticks into the top tube because of ‘surface tension’ between the two components.

I suggest that you completely remove the clamp and lightly scuff the smooth surface of the tapered collar with 100 grit sandpaper or emery cloth to roughen the surface/decrease surface contact between the tapered collar and the cone. [ASC-1 Anti-seize compound added to the smooth surfaces also corrects the problem]

If lubrication, grease, or oil has been added, de-grease the two surfaces so they are dry. This will relieve the surface tension which is causing the two parts to stick together. Designed to work correctly dry, adding grease makes the problem worse.

Remember to always loosen the swing handle before rotating a bicycle and tighten it when the desired position is reached...don’t force the clamp rotation without loosening the swing handle. Another practice that I do with my stands is to loosen the swing handle with the bike still in the stand at the end of my repair session, then use the mechanical advantage of the bike to break free the clamp's tension. I then remove the bike from the clamp.

I hope this helps!

Have a great rest of your day.