Someone made those lines with a pen for some reason. It is considered damage since didn't happen at the BEP (Bureau of Engraving and Printing, where our paper money is made).
Probably a store clerk used a pen on it to see if they were counterfeit, since they prob never saw or heard of a $2 bill.
Unfortunately that is ink from an ink pen. On the first bill ending in 0706, you can see a slight smear at the bottom of the mark. These were damaged after leaving the BEP. The ink is a slightly different color that the ink used by the BEP.
I agree that it's post-BEP pen marking, but it's funny how the lines are so precisely in the same spot and orientation on each note, and all the same approximate length.
