My, admittedly simple, understanding:
Jet engines are most efficient operating at max permitted RPM, subject to operating limits.
Unfortunately, at lower altitudes Temp & pressure limits would be exceeded so, to produce a given amount of thrust eg maximum or some cruise setting, the RPM must be reduced from maximum.
As altitude increases air density reduces so thrust output for a given RPM reduces. To maintain this thrust RPM must be increased. As RPM is increased (but not beyond limits) efficiency rises.
Couple with this, the airframe is designed to be most efficient at a particular Mach No. This will cause a certain amount of drag which in turn will require a certain fixed amount of thrust (all other factors being equal).
As altitude increases with the airframe maintaining an efficient airspeed, the thrust is produced by an engine that operates closer & closer to it's max RPM. Hence overall efficiency rises.
NB: Rate of change of gain in thrust efficiency would have to be greater than rate of change of TAS reduction, with gain in altitude at this 'efficient' Mach No.
Someone please jump in and correct my errors!!