B737 Captain reported an engine surge during climb from an engine that had been written up on the previous flight. Crew reduced thrust until surge/vibrations stopped and returned to the departure airport.

Narrative

Crew met at van well rested after layover (minus daylight savings).Spoke on van about write-up on #1 engine being 'Evaluated' (Maintenance Release Log entry XXXXXXX) as previous day had experienced a ND (Navigation Display)'Flicker' and Fuel indication electrical 'Flicker' (went to zero and restored itself) on Company X XXXX from ZZZZ to ZZZ1.FO randomed at Known Crew Member [checkpoint] so Captain proceeded to aircraft to begin Preflight Procedures and FA brief.Captain set up flight deck while FO performed walk-around.Weather CAVOK with light westerly winds.Pushed on time with XXX SOB (Side of Body) (incl one special [seat] XC; one assigned DH (Dead Head) FA and a retired Company X 777 Captain XXX?? on left side exit row)Taxi and checklist completion normal to Runway XXR 148.0 GW Flaps 1 reduced Thrust Takeoff.Takeoff SOP through cleanup and After TO checklist completion.CA was hand flying passing approx 14;500 feet MSL when PF felt a slight surge and slight left yaw. Assumed left engine; but no indications on engine gauges to confirm. PF disengaged Auto Throttle and began retarding left engine toward idle. PF requested PM inform ATC leveling at 16;000 feet as we began trouble shooting. Once left throttle reached about two inches from idle stop surge/vibration went away; but PF continued to retard left throttle to idle. PF leveled off at 16;000 feet MSL; trimmed for level flight and engaged autopilot.FO/PM had already pulled QRC for 'Engine Limit or Surge or Stall' checklist and was opening Electronic FM for whole checklist.Slowed aircraft to 230 knots clean and requested vectors from ZZZ Approach until we were ready to return to ZZZ.FO/PM ran checklist; computed single engine landing data for about 140 GW after we both confirmed below Max landing weight147.3 GW .Best move by Dispatch was an ACARS msg saying she was monitoring situation and let her know if we needed anything.I asked FO to assume control of aircraft while I called FAs to inform them things were under control and we would be returning toZZZ. Gave abbreviated briefing after ensuring they understood it was just an engine surge.Made a PA announcement to passengers to let them know we would be returning to ZZZ and back on the ground within 20Short ACARS to Dispatch about return to ZZZ.CA re-cruised FMC for 16;000 feet; but forget to reset Pressure controller. (Heat of the moment) FO quickly remedied that when we got the off scheduled descent. (Lesson learned)CA briefed approach and stabilized criteria and let FO know we had and would use both engines should we need to go around. We would fly a visual downwind and landing if required to go-around.ZZZ approach began vectoring us toward visual; backed up with ILS for runway XX Right. (CA thoughts were longest runway; closest to exit for Fire Rescue and would not close primary approach runway) informed tower we would exit at taxiway 1. Flew uneventful 15° Flap; single engine approach and landing. While we could have easily cleared at [Taxiway] 2; we taxied clear at the end [Taxiway] 1 so as to ensure no brake temp issues and that is where we told tower we would exit.Stopped clear of Runway; set brakes and had Fire Chief check number one engine. Fire Rescue reported no signs of problem so we taxied back to the gate to complete paperwork.After parked at gate; a passenger; XXX?? (Retired Company X 777 pilot) came to the cockpit to let us know what he had seen. He was in the left side exit row and was awakened by surge. He looked out window and saw a momentary torch from #1 engine. He stated that some passengers in front of him stated that they saw something flash by their window into the #1 engine.After debriefing Maintenance; FO and I walked outside to look at #1 engine and observed no sign of any damage to the engine cowling or engine blades. No visible signs of any impact (birds?) and nothing on the leading edge of the left wing. Rear section of engine showed no visible damage either.