This looks like a cloth(or similar) strikethrough 1961D LMP

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Sorry to say it but no, this is environmental damage. Looks like a ground find.

 

That's been in the ground for a long time.
Ask yourself: How difficult would it be to be struck through cloth on BOTH SIDES?
Answer: Nearly impossible.

Here is a REAL struck through cloth coin:

 

That is the rare twisted image variety. With a bit of practice, it would look like a normal damaged cent.

 

worse than the normal 'environmental damage'

It's badly corroded

 

Not a struck through anything. It's corroded by the environment.