A Magnetic Misconception on Divergence 0/Closed Field Lines?

Question: Can we ultimately atttribute no work or net zero work done by a magnetic force to the closed magnetic field lines that results in Divergence zero of a magnetic field? That is, is it a misconception to say that closed magnetic field lines imply magnetic force will always result in no net work?

(I meant misconception on my part not theory.)

Edit: Why misconception? Now switch to electric field. The field lines between two opposite electric test charges are also closed and resemble that of a bar magnet, though electric in nature. Does it hold? Is it enough to say that since the field lines are closed between the two test charges that no net work can ever be done?

Work done by a magnetic force on what ? Electric charge ?

Electric charge is all I can see (thinking back to Griffith's book).

Consider the electric field of an idealized electric dipole. It has only closed field lines, but it can do work on a charge.