I am captain awkward when it comes to things like this!
This is something you need to get over and it is the reason you’ve made so many assumptions. Your teen is old enough to have had this discussion with this woman and negotiated a fee and it would have been a good teaching moment if you had supported them in that.
Talk to your child and tell them tha
The whole enterprise seems misguided. The sole purpose was to earn money but that wasn’t discussed and secondly, by driving your child there and back you were doing the heavy lifting in this commitment.
You wanting to help your child is admirable but what do you think they have learnt from this? The conversation about money should have ideally happened before the conversation about tasks. Your child was doing a job but you’ve treated the enterprise as a favour and favours are often not remunerated. What this woman has paid or not paid to others in the past has no bearing on your situation. Would you have agreed to doing work without knowing what you were going to be paid?
What’s done is done but what you can do now is apologise to your child in not supporting them better. Suggest that you and your child do a follow up visit where they can articulate what they have done and can give a short feedback of the job. Which will give them (not you) the opportunity in asking for payment for their endeavours.
DD wasn’t feeling very wel and asked me to let school know she couldn’t go in. The look of panic that came across her face when I said that because she had just turned 18, it was now her responsibility . On the face of it, it was not a complex call but I offered to practice with her before the call to boost her confidence. This is the same DD that has applied for student finance, organised her own health insurance and went to Madrid last year to see Metallica etc with zero input from me.
Treat this as a teaching moment, for you both.