Except they are playing him though, aren't they? Not very much, but he's playing. I somehow doubt they'd waste a roster space, and deny other squad members playing time (scant as it may be) just to "save face". Clearly they think he's an important piece of the squad, otherwise they'd be bringing some other multi-millionaire off the bench.
All things considered, unless you believe MCFC feels some sort of magnanimous duty of care to NYCFC (spoilers: they don't), and would consider jeopardizing their season one iota just to help us out, this is actually the best outcome we can hope for - the less football Frank plays now, the less rest he'll need when the English season finishes.