How to know if it's safe to give credit card info over the phone

I was asked to give my credit card information over the phone  to a collections agency that did not show a safe/secure web page for paying online option.  How do I know if the over the phone information will be safe?  

Is it a red flag to have the manager tell me he's never heard of the standard format using the s after the http and the icon (such as a lock symbol) ?  made me suspicious - even though they had a website and knew what I owed on a student loan?

thanks - Shelly