I accidentally ran a Stihl MS 261 chainsaw on a 4% mixture for 3 tanks instead of the 2% oil to gas mixture it should have had.
Would this have done any damage to the machine should I do anything special to deal with this situation?
I am by no means a small engines expert (and someone should correct me if I'm wrong), but as far as I know, running with extra oil will make it smoke while running and may foul up your spark plug (?) which is easily fixable, but won't cause any permanent damage. Running it with less oil than recommended would mean insufficient lubrication and may damage the engine.
As for "should I do anything special": I'd inspect your spark plug, replace it if it is fouled. Maybe check your fuel filter and replace that if needed.
Stihl's website have a guide for engine oil/fuel mixtures, the following applies to ANY petrol driven chainsaw:
Your petrol-powered engine requires a mixture of petrol and engine oil. The quality of the petrol and oil is extremely important to the running and life of the engine.
Unsuitable fuels or mix ratios that do not comply with the specification can seriously damage the engine (piston seizing, excessive wear.)
The MS 261 in particular is a professional piece of equipment, I would definitely take good care of it and not take any chances.
With 4% 2T mix, it may smoke while running or foul up your spark plug, but nothing to worry. It would not damage your engine.