An action, anointing, lies behind the name of a salve.
Latin unguere meant to anoint and produced unguentum. The ancestry reaches Anglo-French oignement, then Middle English oynement, which was altered towards ointment. The spelling changed while the word remained connected with applying a salve.
The cards omit Latin unguentum. The dictionary describes the French word as ultimately from Latin, so this is a selected ancestry rather than a claim of direct borrowing at every arrow.
Source
Merriam-Webster: ointmentWord History supplies the root verb and selected spellings, with unguentum in the deeper ancestry.