I see what you mean but it looks like a different type of ink to me. I doubt it’s ink from the BEP. I also see no smearing of the BEP ink do I think it’s been applied after it left the BEP.
It is easy for me to say no, but interesting. After thoroughly examining the entire note. There seems to be a crease just above the Secretary's signature where it appears it was caught in something, and an ink line there from the signature to the seal that could be a smear. Where this line crosses the seal, the green ink is removed and there is also ink on the back of the note. May very well be post BEP but is still interesting.