No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Your mortgage is due on the 1st each month.
You can pay them anytime up to the 15th of the month without any penalty. So the 2nd to 15th is considered your grace period. Should your payment be received and credited by your lender be aware that a late fee can be charged. Refer to your originally promissory note, your Final CD or consult with your lender (or read your statement thoroughly) for the amount they're able to charge. I have seen some servicers 'sandbag' those fees to unprospecting customers which can sabotage any refinance opptys or early payoff strategies, so be careful and aware of the day your loan servicer actually credits your account.
With that being said, as long as you pay before the 30th of the month the lender may only charge you that late fee but won't notify the bureaus that your payment is 30 days late which is something you just want to avoid if at all possible, naturally.