It's easy to label people greedy and selfish when you're the one who needs charity. But the babysitter's parents really do have a right to have their gas OR bus fare or whatever compensated. It seems odd that you arranged substandard pay with the teen directly. I'm not saying you bullied her into it by telling a sob story about how you were poor and in a bind, so she'd feel obligated. But it seems like a request for charity should be run past the parents out of courtesy, or it really does look like you're taking advantage of her.
I'd have thought the same thing if I suddenly found out my daughter was roped into a babysitting gig that didn't fairly compensate her.
I don't mind helping a person in a bind, but so often they end up expecting a lot more than they let on. For example... a free babysitting gig that was supposed to be a few hours for an emergency, once turned into an all-day overnight gig, and then she acted like I was supposed to do this every day (and talked as if I had already agreed to such), and the only "compensation" she had in mind was letting me use her washer and dryer (I didn't have one at the time). I've had this happen a lot. Not just with babysitting, but with before-school care and rides. I've been hired to tutor one child and been expected to babysit a whole bunch of children once I got there (which pretty much makes effective tutoring impossible), and then interrogated about the progress.
Now, I am not saying you did this or planned on doing it. But my experience is, a LOT of people do it. And most likely, this teen's mother had similar experiences with people, so she wanted to nip it in the bud. It could have been averted by being upfront with her, because when a minor does any kind of work, it usually does involve some effort on their family's part too.