Yeah, not much to be sorted, it really just comes down to an untrustworthy TA selling you a skiplag ticket and making quite a bit of cash doing so. They'll likely make it impossible to get a refund at this point. If an airline notices and brings this up with you, honestly, you have a pretty good excuse - your travel agent booked it for you without you realizing it was a skiplagged ticket. Airlines have been pretty aware of this issue for a while (especially AA) and know that the passenger often has zero clue of what's really going on.

But if a TA were open about what they were doing, you could have had the option to choose those legs at a different date (perhaps you *do* want to visit Lima within a year, and could separately book a one way LHR-MIA or LHR-JFK later in the year). In fact actually flying those final legs eventually would make this *not* skiplagging and you wouldn't be breaking any rules.

Note that you could have booked exactly the same trip on your own using the "multi-city" booking option on AA's site:



You know, if you really wanted to get more out of it, you could see if BA (or AA?) would let you change the MIA-LIM portion to something within a year out at a reasonable date for you to take a later vacation. I think you're likely going to have time to think about after your trip - you usually should be allowed to change it even after flying the first leg, though I didn't get around to looking into the change fee. You should also be able to change the return to business for an upfare.

Then you'd at least get the rest of your nTP and make another vacation out of those extra legs. I don't know BA's policy on taking over tickets from TA control, but I suspect trying to do it through this sketchy TA may result in additional "service fees" and other questionable charges, so I'd recommend not doing anything through this TA. Plus you would actually not be skiplagging at all or violating any policies by simply taking advantage of the rest of the trip.