請教老師: 我AOS身份申請了失業津, 現州裏要求提供:

1)Working authoriation(I have EAD, but I was still in H1b visa last month).
2)Documentation includes alien registration number.(I have AOS document)
3)Complete and sign the certification saying:
I hereby certify, under penalty of perjury, that I __am __am not in satisfactory immigration status. My country of nationality is ________.
They also need INS to provide my alien status for purpose of determing my eligibilitgy for 失業津.
Now teacher, tell me how should I do:
a) reply the letter but I am afraid INS will know I am unemployed so far.
b) If dont reply, state government will deny my application, will INS also know this??
c) can I revoke my unemployment benefit claim?? Since I read teacher Pjiang's blog saying this is 'Public Charge', it will adversely affect my I485.
Thanks so much for your kind urgent advice!