No, but whether or not the page is secure has ABSOLUTELY NOTHING to do with whether your information is secure.
Are you familiar with what happened to Magic Vacation Title a few months ago? Their portal for transmitting payment information was 'secure' - but their e-mail server was not!
They got hacked.
Afterwards, during the investigation, it was plain that *** was not following ANY security protocols with regard to customer information. They weren't deleting previously received data - nor was it being encrypted. It was ALL stored in plain text and easy to read image files. Consequently the hackers where able to send out fake payment e-mails to hundreds/thousands of customers and former customers. ANYONE who had previously done business with them had to cancel/change credit card numbers. It was a mess.
So if you really want to be secure, provide the info over the phone - or better yet - ask them what they're doing with your data once you've sent it. The correct answer is deleting it (with no copies) or encrypting it. Oh - and don't settle for the answer 'I really don't know' - because the person you speak with that handles receiving payments won't have a clue about what happens to your data.