Mooney M20K Pilot reported experiencing engine trouble on climb out and immediately returned to the airport. Upon inspection; it was discovered the propeller tips were bent; likely from an earlier bounced landing; and was missed on preflight.

Narrative

Originating flight from ZZZ; one passenger. Flight uneventful. Obtained ATIS at destination facility with tower instructions for left downwind Runway XX. Did feel my pattern altitude 200 feet low. Approach felt stabilized. At time of landing; I had appropriate landing speed. I flared too high and plane dropped/bounced twice. I put full power in for go around and had difficulty maintaining control but was subsequently able to complete return to pattern and safe landing. On review of ForeFlight track log my landing speed likely had decayed too much as well but difficult to ascertain if this was during or after the bounce.After parking at ramp; my wife and I went into town for about 2 hours and returned to depart from ZZZ1 with plan for return leg to home field ZZZ. Run up was good; upon take off from Runway XX; engine sounded good however shortly after take off; power was erratic and I immediately contacted Tower with approval to perform teardrop and return to land on Runway XY. Was able to straighten my return approach; despite pulling power back engine was not responding to input and was maintaining too much power to descend. I had to pull mixture out to descend and was able to land safely although Tower did notify me to extend landing gear.After landing found all prop edges bent which I had failed to notice prior to take off. To prevent/remedy; I would have watched my landing airspeed much more closely and not flared too high or too much. Secondly; after such a landing I would have done better pre-flight and in particular looked at the prop.