2004 D Penny Finger Feeder Error?

Not Feeder Finger Damage. As ijn1944 stated, probably a finger or palm print.
This is why we always advise holding coins by the edge.
Also if you straightened out the rotation of the cent, the
date would be straight. you have it on an angle

FYI
Feeder Finger Damage usually only shows on the field of
the coin, not on the relief. It also usually shows on the
anvil die (reverse) of the coin.

It's odd that you can feel the lines.

I agree that they aren't feeder finger die scrapes.
Feeder Finger die scrapes are parallel to each other and show up where design meets the field.
Some of these lines are on top of the bust (which is the deepes r part of the die) and aren't parallel to each other.

Maybe it was an oily palm print, as others have said, or from fabric stuck to the surface, giving it a raised texture you can feel.