It all started with this paper - arxiv.org/abs/1801.10246 - the 3rd in a trilogy. Claimed that a correction due to Earth's gravity should alleviate tension between theory and experiment:
Looks like gravitational corrections to the muon #gminus2 are not as large as claimed in the original paper...
Even if you accept the calculation, these corrections would be much too small to measure (and are already taken into account in the systematics...)