Cleaning in this case means removing any dirt, grease, loose grit, loose rust, mortar, etc.
Do not use caulk or mortar, as these are not the proper material for this application. The tendon end should be covered / sealed with non-shrink grout (sometimes referred to as hydraulic cement).
You want to prevent the tendon end from being exposed to moisture because capillary action will craw it into the slab between strands where it can eventually cause failure of the tendon. Do not worry about the two cut off nails at either side of the tendon, just the tendon itself.