Can the manual shifter on a 1981 F150 4 speed overdrive be removed?

 

You must be talking about the floor shifter, gain access to rubber boot by loosening carpet at passenger door and lifting up. Most likely, the retainer for the shifter is the push in and turn collar. Similar to a light bulg with the round base, align the pins, push in and turn. The shifter collar is the same, I would use a large pair of slip joint pliers, commonly miscalled Channelocks. Let the teeth of the pliers grip the collar, push down slightly and twist counter clockwise. To install reverse direction of twist.