Matt,
What a good "plant parent" you are, to be so worried!
You should be fine. Yes, there may be a tiny amount of grease particles in the water, but, for example, a lot of dormant oils have petroleum products in them, and folks put a lot of dormant oil on plants and they do fine. The tiny amount you had on your hands should have no effect at all, unless there was a LOT of grease, and you were watering very tiny, delicate seedlings. Even then, it probably won't affect them adversely.
I have watered my plants before with hand lotion on, for example, and could tell that hand lotion was getting into the water, and it never caused any problems. Grease shouldn't bother them at all (maybe keep some insects away if you are lucky, but that is doubtful).
Happy watering!
Carolyn