Can immunomodulators cause bruising? What else can cause painless bruising of unknown etiology?

Possibly. Some immunomodulators can cause low platelet #s which can lead to bruising as well as bleeding.
Possibly. Not knowing what you are taking or why you are taking it, makes it hard to say specifically. Some immunomodulators affect the blood system of the body, possibly giving you anemia or affecting the way your blood clots. Please contact the doctor who put you on the medication and tell them about your symptoms without delay.