This is a just a math game.

the loan amount as 223k or 222k (or any other loan amount).

The difference is the escrow payment you will have at the closing. For your case, if you chose to have loan amount 222k, then the escrow payment at the closing will be $1000 more.

For the same reason, you can choose 200k as the loan amount, then your escrow payment will be 23k more.

These are just numbers. The important thing is that the closing cost will be paid by the agent, that's why RE8888 said you need to check GFE to see whether the agent covered the NRCC.