The concentric gaps and rings commonly observed in protoplanetary disks in millimeter continuum emission have lent the impression that planet formation generally proceeds within orderly, isolated systems. While deep observations of spatially resolved molecular emission have been comparatively limited, they are increasingly suggesting that some disks interact with their surroundings while planet formation is underway. We present an analysis of complex features identified around GM Aur in $^{12}$CO $J=2-1$ images at a spatial resolution of $sim40$ au. In addition to a Keplerian disk extending to a radius of $sim550$ au, the CO emission traces flocculent spiral arms out to radii of $sim$1200 au, a tail extending $sim1800$ au southwest of GM Aur, and diffuse structures extending from the north side of the disk up to radii of $sim1900$ au. The diffuse structures coincide with a dust ribbon previously identified in scattered light. The large-scale asymmetric gas features present a striking contrast with the mostly axisymmetric, multi-ringed millimeter continuum tracing the pebble disk. We hypothesize that GM Aurs complex gas structures result from late infall of remnant envelope or cloud material onto the disk. The morphological similarities to the SU Aur and AB Aur systems, which are also located in the L1517 cloud, provide additional support to a scenario in which interactions with the environment are playing a role in regulating the distribution and transport of material in all three of these Class II disk systems. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.