IF you are NOT on the dining plan then you WILL be charged the full amount of CRT. CRT is a PREPAID meal, not just a hold.
IF you ARE on the dining plan, then the card will be taken but not charged.
Honestly, it sounds like your travel agent goofed in some way. Either she didn't mention to the phone agent that you needed it on the DDP or she may have booked online. There is a well known bug on the online dining that sometimes does not see the DDP on a resort reservation and charges the card for a pre paid meal.
Since your agent requested a refund now, they did have to cancel your ressie to do so. This means you give up that slot. Your agent should have known this. What they should have done is not canceled the reservation and you could have received a credit at the restaurant (including possibly having it put on a gift card that you could have used in the parks).
Your travel agent should be responsible for the difference in the cost because THEY made the mistake to approve the refund then.
I agree it's the TAs fault.
I know you mentioned other ADRs, but unless you are doing dinner shows, CRT is the only restaurant that has prepaid meals, so this wouldn't be an issue with any other ADRs.
If the TA did it online: then it would clearly say whether it would be a hold on the card or actually charge the card. The bug that charges dining plan people for CRT instead of putting a hold is well known (or at least a TA should know of it). So, when the TA went to check out, if it worked correctly it would say $0 is owed. if not, itwould say $$$ is owed. The TA should have known nothing should have to be paid, and called disney dining to complete the ADR for you.
If it was done on the phone: it should have been very clear whether or not the CC will be charged or just used as a hold. If it was by phone, I think it very unlikely that the TA said it was on dining plan, confirmed with the CM that the CC would not be charged, and then the CC was charged. If that happened, then it would actually be CC fraud on Disney's part. When I called disney dining, the CM were always VERY clear they would be charging my card. So, if the TA called, the TA knew your CC was going to be charged, so the TA messed up.
As for getting it corrected, the TA should have known that the original ADR would have to be cancelled and a new one made (and it couldn't just be fixed on the phone). The TA should have known to have the CM try to book CRT with the dining plan at a good time, and if they were successful, THEN cancel the original CRT. If they couldn't book a new ADR at a good time, the TA should have known of the option to have your CC refunded at the time of your reservation and putting the meal on the dining plan. The TA should have given you the option of doing this, or risk losing your perfect ADR time, before taking that risk.
As for the $20 exchange rate loss: I agree the TA should cover it for messing up. It was a refund, and should not have been processed as a reversal of charges. It is not Disney's fault the CRT meals were purchased by mistake. They should not have to eat the $20 on the exchange rate change. The TA should eat it for messing up.