I think that the rules require that a priest obtain, and return, the hosts from the tabernacle during mass. However this seems to be commonly ignored, with the bishop’s at least implicit approval.
On the other hand, EMHC’s who are taking the Eucharist to the sick, may retrieve and return hosts to the tabernacle, if it is not convenient to receive them from a priest or EMHC at Communion time in the mass.
I prefer to obtain hosts at Communion time to preserve the linkage of the sick call to the mass. However, it is almost never convenient to return an unused host at Communion time. Returning them to the tabernacle is much preferred to the alternative of the EMHC consuming them.