Can I message the people who saved my card?

Yes, with Pro, which is $0.99 a month. How you reach somebody depends on what they did with your card.

• They allowed notifications from your card: send them a notification from Notify. It arrives on their lock screen. See Sending a notification.
• They added your wallet pass: put a message on the pass from the Wallet screen. This needs the Pro + Wallet plan. See Sending a message to everyone holding your pass.
• They wrote to your WhatsApp number: with the WhatsApp add-on you can follow up from your own number. See Who can I message?.
• They only sent you the Stay in touch form: their phone number and email are on People, so you can call or write to them yourself.

Somebody who only opened your card, and did none of these, cannot be reached. There is no list to buy and no way to message a stranger.

Each notification and each pass message costs one message credit for every person it reaches. See What is a message credit?.