Literally, '
other grooming'
In the field of zoology, allogrooming refers to all social grooming that takes place between members of the same species. Social grooming may be done for hygiene, to calm, for conflict resolution, and to form social bonds; with the possible exception of grooming for hygiene, for most species most of the time allogrooming or autogrooming (self grooming) is the default form of grooming.
Most interspecies grooming takes the form of cleaning symbiosis, and to the best of my knowledge there is no paired counter term to allogroom (e.g. 'exogroom') to refer to this.