They should add something like "Create", "modify" and "Drop" linked servers, i think that should be the way to go.
In our case, we had to give it to the IT sec team and there isn't a permission for it.. we had to give them the sysadmin role (i know this is the biggest mistake ever) their job basically is manage Linked Servers (because of their nature, connecting to others engines) and create users and add permissions.... we have a bunch of stuff for audit and triggers to stop drop tables and drop databases but that still makes me uncomfortable, audits also for DBCC commands, alters inside databases. etc etc. but still i think they have way too much power, and they are not even DBAs.
but i'm just the junior DBA so my opinion is not that important ¯\_(?)_/¯