This is repeatable here.
Save a named Cplane with the dialog floating.
! _-NamedCPlane _Visible _Visible _Toggle _Enter _Enter
The highlighted named Cplane icon shows as expected.
Close the dialog and it disappears as expected.
Turn on the Cplane grid
_NoEcho _-DocumentProperties _Grid _ShowGrid=_Yes !
The named Cplane icon re-appears and remains displayed until the next Cplane change.