Your place looks clean, tidy, well decorated, really nice, you look like a lovely lady, etc. … BUT the place also looks really closed in: no windows, no light, no air. To me this can very clearly be seen in the pictures. Personally I prefer a space with more natural light and air, but could possibly be enticed into booking if the price is right.
In this case, with the third party booking, the guests of course didn’t know where they would be arriving. My guess is that in Barbados they have a very light and airy house, and in your place they might just feel claustrophobic. And of course, there is no quick solution to this problem.
All this however, shouldn’t have to be your problem. The pictures clearly show that it’s a space with little natural light and one can suspect that natural ventilation is limited. There is even a review that mentions the darkness of your listing.
The only remark I can make: Doesn’t AirBnB want us to photograph our listing with natural light only? (To be honest, although our rooms are quite to very light, we still made pictures with some lights on.)
Apart from that, you are of course in the same 
situation as we are currently. If you don’t accept the refund, you will probably get a very bad review. If you do refund, you will probably still get a lousy one.
This is clearly a major flaw in the review system. The whole situation is solely the responsibility of the guest (or the person who booked) and now you would have to assume that responsibility if you don’t want to harm your business. It’s so unfair.
You could try doing what we are trying to do (see topic First non-reader complaining and wanting refund), although there’s some risk involved and it’s not really ethical to be lying to people. On the other hand, this kind of review system isn’t ethical either.
EDIT: Please do take care when attempting this, because in your case AirBnB is already majorly involved.