The confirmation dialog says their team will be in touch within 24 hours, so the first check is the inbox you gave them. Beyond that, search your own name on PropertyChecker after about a week. InfoPay's California filing reports a six-day median on deletion requests across its thirteen domains, so a week is a fair first check and thirty days is the point to escalate.
If the listing is still up, email privacy@propertychecker.com with the submission date. That address is published on the opt-out page itself, and the filed compliance contact at compliance@infopay.com is the escalation above it.