Unlikely to cause any damage if it’s a very small leak unless the coolant has entered the bearings on the timing belt pulleys, the coolant will have evaporated off and left a residue, make sure this gets cleaned properly.
If they need to remove the timing belt make sure it’s fitted back in the same position (not reversed) unless they renew it.
IMO if the mechanic has damaged the water pump O ring when installing the pump, failed to fill the coolant to check before re-assembling the timing gear you might want to use a different garage in the future.