As a first option, I would try to resolve this with a phone call.
If that didn’t work, I would be sending them a letter asking them to:
a) explain why they called the EGM in the first place
b) why they did not consult with the committee beforehand
c) why they thought it appropriate to charge for a meeting that was not required and not held.
It may be that they technically have the authority to do any or all of these things but that doesn’t mean they should, just because they can
If your committee agrees, I would also say that the committee considers this a serious breach of trust and reserves the right to take this matter further if a satisfactory resolution is not reached.