Normally there are two parts to the FSY payment. The youth (or family) pay $75 directly to the church when registering for FSY. If the youth withdraws in time then this portion should be refunded automatically by the church and the ward shouldn't need to do anything but it may take 6 weeks to process (see
https://www.churchofjesuschrist.org/you ... s?lang=eng).
The ward is also responsible for paying $75 for each participant. The family should not be asked to contribute to pay this portion so there should not be any refund required here.
The tricky part happens if the ward needs to pay a part of the $75 the youth/family is responsible for. In that case the bishop marks this fact when declaring the youth eligible for FSY and the youth won't be charged when registering. The ward will be charged the youth's $75 in addition to the wards $75. The family may then contribute however much the bishop decides is appropriate and puts that amount in the FSY budget category.
Assuming the latter applies in this case, then just make a payment back to the family for the amount they paid from the FSY category. Include documentation indicating that it's a refund and reference the original deposit.
This page has specific information on how refunds are handled although it doesn't mention about a ward refunding a partial payment:
https://www.churchofjesuschrist.org/you ... n?lang=eng
I can't find anything that specifically authorizes returning camp or FSY payments but it was specifically authorized with the old Other:AMFA categories. Plus payments to budget are not tax deductible so they aren't counted as charitable donations that can't be returned. It only makes sense that if someone pays and can't go (especially if they withdraw ahead of time), that their payment should be refunded.