It will have no effect on the pan on most cooking surfaces, but cleaning will allow copper conductivity to work properly.
Cleaning is a bit of work, but I have the exact same pan and had the same problem. First, to handle the real hard burnt on grease and crud, I purchased a copper wire scrub pad and a stainless steel scrub pad. You can find these in most houseware stores, or houseware section in a supermarket or drugstores. The copper is used only on the copper part and will not cause it to be rubbed off or scratched, the steel for the steel part with same effect. As a scrubbing agent I used Bar Keepers Friend. This will require elbow grease and may need multiple applications, but take your time, be firm but gentle and keep going while rinsing in between with very hot water. Also, make sure scrubbers are wet with hot water while scrubbing. It sounds tedious, but I just got into a zen mode and relaxed into it and enjoyed the results. It got it all off for me, and mine was 10 years of accumulation.
After you've scrub off the hard stuff, take some kosher salt and pour in bowl, then dip half a lemon into salt and scrub the copper with the salted lemon. You can also just pour salt on pot and scrub with lemon, this will give it some additional scouring and will bring back that store bought copper shine. To keep it clean going forward, clean it immediately after each use, using pads if necessary, and a lemon scrubbing when dull.