There’s a gasket to keep dirt out of the area. Oil is kept in by a seal on the transmission output shaft, and another seal on the transfer case input shaft. Between those two seals the space is dry. Or should be.
I recently had the same work done and the transfer case input shaft immediately started leaking. Seals harden with age and lose flexibility. Disturbing them can cause a leak.
You’ll need to drop the transfer case and ascertain whether the leak is from the new transmission (unlikely) or the transfer case input seal.
If I were doing another trans replacement tomorrow, I’d tell the shop to include new input and rear output seals for the transfer case in the work. Easy to do while it’s out.
PS- if you’re having a shop do the work, I’d go back to the transmission guys and ask them to address it and give me a break on the cost, since it’s either a warranty on the trans OR a secondary leak caused by their work. In my case the shop found the leak before I did, and we agreed I’d pay for the extra parts, and they would absorb the labor. A shop that does a lot of trans work should IMO anticipate secondary issues such as this.