So I picked up this little mini beauty in the supermarket a couple of days ago. One flower was already a little wilted but a couple are now wilting (only on one stem interestingly) . It was pretty dry when I bought it so I gave it a water.
Are you supposed to dead head at all or just let them do their thing?
It's not going to make any difference to the plant. If you leave the wilted blossoms, they will fall off eventually anyway. If you don't like the look, snip them off without yanking on the stem.
If you feel you must remove the flowers, do not cut living tissue with unsterilized cutters, it could cause problems with infections.
It is easier to just leave them alone until all the living tissue of the flowers and the spike dies off naturally, then you don't have to sterilize cutters.