YES! Your credit card and details are absolutely safe with Strikingly.
Strikingly uses Recurly as our payment system and it’s PCI-DSS Level 1 compliant (which is top-level for security). Your payment and card information goes to Recurly directly and doesn’t go through our server at all. You can check out this article about security with Recurly.
If you have other concerns, feel free to send us an email through firstname.lastname@example.org or chat with us.