If you don’t see screw holes or screws on the posts, try lightly pulling the bases of the posts away from the wall. They may slide up on the post and expose hidden screws. If not, then the towel bar is held on with adhesives. If there is small slot in the bottoms of the posts but can’t see a screw inside, then the towel bar has tabs that you need to press down to remove it.
If the towel bar still sticks to the wall, then loosen the screws more since they’re still catching on the wall brackets.
Some brackets are screwed directly into your wall while others may screw into a wall anchor in your drywall. You can pull out the wall anchor carefully with a pair of needlenose pliers.
Some towel bars without set screws have a specific way to adjust and remove by twisting the side mounts horizontally away from the bar.
If the bar doesn’t come off easily, ask a helper to release the tab on the second post so you can remove both posts and the bar at the same time. Make sure the bar is pushed all the way to the opposite end from the side you are trying to remove.
If you plan on installing a new towel bar, then you may be able to reuse the brackets.
Adhesive used to secure towel bars is heavy-duty, so there’s a chance that it could damage the wall underneath when you remove it. You’ll reduce the risk of damage as long as you work slowly and carefully.