Since Recurly v4 adds fields in using iframes, there is a limit on what styling can occur. So when trying to style borders it isn't clear whether it is possible to change the borders.
Associated links : https://dev.recurly.com/docs/getting-started-1#section-styling-card-fields
Styling of the hosted billing information fields can be controlled through the .recurl-hosted-field sections of the CSS file as shown in this example: https://github.com/recurly/recurly-js-examples/blob/master/public/minimal/style.css#L191-L218.
This includes changing of field size, border size, color and other attributes