First of all relax! Its just a late payment not a fraud or felony charge!
1. As you have cleared your dues, ask Paytm to update your CIBIL account at earliest. They may not remove late payment remark however your account should be marked as fully paid and settled.
2. 172 day late payment will have only temporary impact. In next 2-3 months you will see your CIBIL score increase (provided point 1 is completed)
3. Dont hurry to get any CC now. You will get crappy offers or have to get secured card. Wait for 3-4 months. Let CIBIL get adjusted. Remember - Reason for card rejection is NOT 172 day late payment - its because its still showing as open account and hence banks treat it as default (until cleared)
4. Even if 5 day old late payment reflects on CIBIL, banks will refuse credit card until its cleared.
So long story short - just hold on and avoid getting useless secured cards.