If you're conversant with electricity, here would be my troubleshooting schedule: Disconnect converter and power circuit breaker back to "On". This is to isolate that the converter is the source of the problem and not any other circuit wiring. If the GFCI trips when converter is disconnected, the problem lies in associated AC wiring on that branch circuit shared with the converter.
If you plugged in a vacuum cleaner or a heater or any other device that is on the converter circuit, check those receptacles first. A loose neutral or ground in a receptacle will trip a GFCI, occasionally.
Also, as a matter of preventative maintenance, the neutral wires in the load center should be tightened on the bus bar. The ground where it connects inside load center and on the frame should be checked as well.
