PayPal's invoice email says "You don't have any payments with this seller in the last year." The invoice page usually does not, so HangUp cannot see your payment history. Tick this only if you want HangUp to assume you have never paid the seller: invoices that say almost nothing except a phone number are then held back more often. It can make HangUp stricter, never more lenient. Off by default.
The extension sends the seller-written text of the PayPal invoice page you have open (or of a PayPal invoice email open in Gmail) to this server to be checked. Use only a server you trust.