I overfilled my engine oil by a quart. Will that cause damage?
Just drain a quart out and eliminate the possibility of damage.
If you drive it possibly.
From NAPA:
In most vehicles, the crankshaft that drives the engine’s pistons sits just above the oil reservoir located at the bottom of the oil pan. In order to move lubricant throughout the motor, a pump pressurizes it and draws it up from the pan (or sump), so it can be sprayed in key areas. Overfilling engine oil can raise the level of oil in the pan to the point where the crankshaft starts to make significant contact with the reservoir. Since it moves so fast, it can turn the oil from a liquid into a froth that the pump is no longer able to siphon and distribute. At that point, the engine can starve from lubricant to the degree that serious damage is often the end result.
You can withdraw a quart through the dipstick tube.