To wish people would stop telling me things in confidence

[Emphasise]

Today, someone who works at my DC school told me something about another child's progress that her parent should know but of course "please don't say anything"

Basically child has a delay and parents are paying for help privately. In the opinion of the "teller" the child isn't ready for this help (because of his delay) is making no progress/can't be expected to make progress. She thinks the professional is a charlatan for taking their money knowing that they can't help. The school staff member is qualified to know IYSWIM, whilst they are very much talking out of turn, they do know what they're talking about.

Probably I should report the school employee, but I won't. Would you say anything to parent?

No.

And I'm be very angry with the school employee (assume it's the senco) she absolutely shouldn't have said that to you about another child. I wouldn't report either, but I'd go back to the senco and tell her how inappropriate she was and what an awkward position she's put you in.

How well do you know the other child/parents?

Well enough that I'd expect her to tell me chastened.

If she is talking about this child to you how can you be sure that she isn't talking about your child to others. Definitely report as inappropriate.

Is the child enjoying the environment ...? is the child happy ....? is the child likely to be upset by being moved to another class/school ?
Does the child have friends in this class ?

who would be most affected by sharing this information .... would it be a positive or negative effect on the child ... ?

That's incredibly unfair and unprofessional to unburden on to you. Is pressuring the teller into telling the parent a feasible option?

She shouldn't have said anything to you. You should report her. How would you feel if it was your child she was talking about to other parents? If it was your decisions as a parent that she was questioning to another person?