If the original nut was fine to begin with and was only raised, it should be a simple matter
of removing the shim material. With the strings removed, try to carefully remove the nut
from the slot. Hopefully, it was only being held in place by string tension. If it was glued,
and glued properly, it should break loose with little force. But try to avoid breaking the
nut. It may very well be perfectly usable after removing the shim. Don't try to remove it
if you're not sure you can remove it without damage.
Actually, it looks like the nut may be above and free of the slot. Still, avoid bending or
twisting it. Remove all the shim material and clean out the nut slot in the neck and the
bottom of the nut of any glue if present. Then set the nut back in the slot, string it up
again, using the string tension to hold the nut in place. Check the action at the open strings.
If good, just glue the nut back in using just a couple tiny dots of wood glue at a couple places
in the nut slot.
Also, the ball ends of the strings are spaced off the bridge plate tail with nuts. If you keep
those strings, leave the nuts on there. If you remove them, you will have a kink in the
active length of the strings (the part that vibrates). Leave those nuts off when you
replace the strings.
What you need to do is not that difficult. Unless you need a new nut or the neck is bad,
you can get all the information you need right here in the forum.