Can having gallstones cause pitting edema on both legs?

I do not think that having gallstones could cause bilateral pitting edema, however gallstones are more likely to be seen in overweight and obese people so also is pitting edema more likely occur in the same group of people. There is no direct pathway for both to occur, but could have associations for different reasons like being overweight or abnormalities in the liver processes.

Very less likely. You should have a complete blood and urine tests for ruling out any systemic disease, especially kidney disease, as the etiology of bilateral pitting edema of the legs. Heart disease can cause leg edema but other symptoms will present first, especially shortness of breath on exertion or orthopnea (shortness of breath on supine position).