if it's a personal check

I guess it is a personal check, and amount not big. the person who pays you do not pay employer tax for you, he did not report the hirement, then no impact on your GC.

if you did not give your SSN to your employer, he has no way to pay employer tax for you.

if it's a paycheck (not possiable for F2), it means you employer payed employer tax for you, you got pay employee tax.