Oh, yes, this is a scam. No person in their right mind would ask and trust a stranger to cash a check that was issued by accident for 31 hundred dollars extra. Because a normal person would stop payment on the check and issue another one in the correct amount.
This silly story about sending you the wrong amount of money is pure bullshit.
They hope you cash the check and give the difference back to them. Then, they disappear into the wood work, your bank notifies you that the check bounced and therefore, you are out $3100.00 because you will owe that amount to your bank.
Sure you can cash the check, but there will be consequences as it is considered fraud and you could be in trouble for conspiracy because you played your part in the scam by using your checking account .