So they hold your info and link for however long the chargeback period is (or the average one, probably 30-60 days is fine) and then lose it.
If you're more worried about privacy than convenience they offer other payment methods:
Which payment methods do you accept? We accept cash, Bitcoin, Bitcoin Cash, Monero, bank wire, credit card, PayPal, Swish, Giropay, Eps transfer, Bancontact, iDEAL, and Przelewy24.
https://mullvad.net/en/pricing/
And you can pay for a decade in advance.
(What is Pretzel24 I wonder?)
"przelewy" means "wire transfers" in Polish: https://en.wiktionary.org/wiki/przelew Nothing to do with pretzels. :)
Also, they do actually keep a link for 40 days, but it seems like some card card networks allow chargebacks past that.