Heat transfer from, or to, a large heat reservoir is always reversible?

How is the heat exchange reversible if a reservoir is at constant temperature? Can anyone please help me. I'm getting confused. Thank you.

Heat transfer is irreversible when it occurs over a temperature gradient. There are no temperature gradients within an ideal thermal reservoir. So heat transfer to or from an ideal thermal reservoir is reversible. However, this only applies to the reservoir, and not necessarily the system that is exchanging heat with the reservoir.

For the heat transfer to be considered reversible with respect to the system, the temperature difference between the system and reservoir must be infinitesimal. If a temperature gradient exists at the boundary, heat transfer across that gradient is an irreversible process that generates entropy. Since no gradients exist in an ideal thermal reservoir the temperature gradient is considered to exist within the system. Therefore, all the entropy generated for an irreversible process is assumed to occur within the system, and none in the reservoir.

Hope this helps.