Very interesting. The note did a 3rd printing pass, but was insufficiently inked. You can see the embossing of the federal reserve bank's district numbers in the four corners. It appears to be "11" which corresponds to Dallas. I am inclined to think it is genuine, because any attempts at remove the ink would have compromised the embossing. Make sure you do not put it in a book or press it accidentally. The embossing (raised imprint) is very valuable, especially in a note like this. I don't have my guide book to errors, so I can't look up the book value right now. But I'll post an update later tonight if someone else doesn't chime in first.
United States Paper Money Errors has a 1981 $20 note at $500 in Crisp Uncirculated. You might be able to surpass that value if the note grades in the high 60s.
Get it graded by PCGS or PMG. The ways to do that is to see if you can "piggyback" on a local coin shop's submission, or join one of the groups yourself for the ability to send it in. TBH, i choose PMG over PCGS and have heard that they have shorter turnaround times right now. You will get the most money from error collectors such as myself if it is graded since 1) We know it is a geniune error and not someone who had tampered with it at one time with chemicals and 2) We know the grade and can negotiate price fairly quickly and accurately.
Not only can I see the 11 district designator's funkee has pointed out, but I can also see the stamp imprint of the district seal itself; just slightly higher than where it should normally be. Would we really be able to see those stamp marks if the error was in fact legitimate??
The embossing leads me to believe the notes did get a 3rd printing pass, but it was insufficiently inked. Essentially the impression cylinder pushed the sheet against the printing plate, causing the embossing but the lack of ink resulted in this note.