Irving Tannen wearing Nuke clothing in 1986H.
Nuke was a brand of clothing seen in 1986H. The improved Irving Tannen was seen wearing a sweatshirt with this company's name on it.
The company's logo was an atom with three rings above the word Nuke in all capital letters.
Behind the scenes[]
This appears to be a reference to Nike sports apparel, for reasons of avoiding copyright, as well as an homage to the nuclear background of the first film and its scripts.