Hi smyfigs,
could you add your usda zone in your signature or profile ?
I don't think that tea will deter a deer or a suede . If a whole big leaf is gone, you have a big one/pest coming to your tree... Could be a raccoon... I don't think that insects will rip a whole leaf.
I had slugs chew on some leaves and the fig-moth too. But they don't take a full leaf. They take bits of it.
I just applied (extinct) lime to the trunks of my trees this week. It deters ants, slugs, moths/caterpillars ... Lime is mainly calcium, and the trees need it too (as always use a bit, not a truck load) .
You should try to identify the pest, before you know how to get rid of it.
If you spread lime around your trees and on their trunks, it will probably help for walking and climbing pests, as lime will sticks to their paws.