C-152 Flight Instructor with student on training flight reported engine malfunction inflight.

Narrative

On Day 0; I was flying the aircraft with the tail number Aircraft X. The aircraft is a Cessna 152 and the flight was operated under PART 91 Instructional Flight. During engine run up; my student and I noticed that the Right magneto was fouled; hence we followed proper clean-up procedure like we have done countless times in the past. Everything resumed normal; so we departed ZZZ via Runway XXR with a departure request of 'Left turn over the river.' Shortly after departing; I told my student that she missed a checklist item of 'Departure Brief' so I intentionally made her return to the airport; taxi to runup area and brief me. Since this student was taking her checkride the next day; I wanted to hold her to a higher standard. The incident took place on the second departure on the same runway with the same request. Upon reaching the practice area and reaching about 2700 MSL; I noticed the RPM gauge needle went from 2300 RPM to about 1800 RPM for less than a second and it resumed normal operations. My first thought was my student must have been messing with the throttle; so I asked her and she said no; also showing me her right hand which had the throttle in full open position. At that point I had a bad feeling so I tuned into ZZZ Tower and requested inbound due to engine roughness. The reason I reported roughness was to let the controllers have a heads up that my situation could possibly worsen so they might be a little more alert. The Tower asked if I was [requesting priority handling] to which I replied no since I had good control of my plane and the engine sputters every now and then but it was still flying. I did make sure that the mixture was full rich. Upon approaching midfield; Tower [gave priority] for me and asked my fuel and souls on board. Right after I answered; my engine suffered from partial power. My RPM gauge now shows 1700RPM even at full throttle. My first instinct was to pitch for best glide and already had XXR in my mind to land. I made sure the fuel selector was on ON position; verify that the mixture is full rich even though I already enriched it prior to returning; and pulled to activate the carb heat. The only thing I did not do was check the mags since I didn't know if that would worsen my situation. I also did not [request priority handling] since it was already [requested] and I landed safely on XXR. Upon exiting; I did let the Ground Controller know that no further assistance was required and my plane did taxi to parking. I did not receive any information so I asked a police officer for the Tower phone number and called them. I offered my phone number; and full name. The mechanics said that the Cylinder Ring was broke and the grove was badly damaged. They said I was smart to have returned on the initial rpm dropped because it could have been worse. I have the pictures of the damage after the engine was torn down. My learning experience definitely is huge! I was so glad I trusted my gut feeling and returned. However; next time I will [request priority handling] sooner. I shouldn't have been hesitant about it; and I was amazed on how the controllers made sure I came in safe. I need to get these guys donuts and coffee. I'm glad I remembered my training but also will communicate more next time. I was more focused on getting down safely which I'm glad that no one was injured and the plane was in one piece.