How to Repair a Bathtub Drain Overflow Faceplate that has No Screws
The faceplate for a bathtub overflow is located on the sidewall of the tub right below the faucet. The faceplate usually has a lever that controls a drain stopper. The holes of the overflow that allow water to drain as it rises are usually located on the edge of the faceplate at the four o’clock and eight o’clock positions. Most of the time the overflow faceplate is attached using screws, in some cases, however it may be secured using caulk. Removing a caulked faceplate will take about ½ hour.
1.  Spray a penetrating catalyst around the entire edge of the entire overflow faceplate. Let the faceplate soak for 20 minutes. The penetrating catalyst will soften the caulk and make it easier to remove the faceplate.
2.  Score around the edge of the faceplate using a common utility knife. Running the knife between the faceplate and the tub  be careful not to scratch the surface of the bathtub.
3. Â is to slide a putty knife underneath the edge of the faceplate and try to pry the faceplate off. Moving the knife around the circumference of the faceplate and prying in every location. Also you can use your utility knife again in locations that seem stuck. Keep repeating the process working the faceplate off the sidewall of the bathtub.
Finally clean the area where the faceplate was located with the penetrating catalyst and an old rag to remove residual caulk and dirt.
Good Luck 🙂