Transmission noise

Transmission with 116,000 miles makes a zing zit zing zit noise on a cold start.

Started after a 5 week sit during the winter. Now every cold start produces a zit zit zit noise. Some last 2/3 seconds some 5/6 seconds. Then all seems well. No noise after the cold start. Dealer replaced starter amd “FLYEHEEL” at great expense. First start after the repair? SAME NOISE, so car went back to dealer. They had the vehicle 4 weeks while I was out of state and all they could tell me was it it the transmission and the noise will not hurt it. Live with it. To mess with the transmission would open a can of worms so they recomend I do nothing more!!!I worked for partial refund and took car home. Still making noise. Info on net suggest to me that it could be a bad oil pump for the tranny. Or maybe a diaphram or valve in the pump that allows the fluid to drain down instead of keeping all the parts covered with the tran fluid. What do you think??? What is my next plan?

What kind of vehicle are we talking about here??? Year, Make, Model, Engine size for starters…Automatic or manual transmission???

transman