How do I prevent membership renewal reminders originating from VERP addresses?
Testing this on v4.6.3, you can define the reply address for a scheduled reminder by editing it at Administer > Communications > Schedule Reminders (civicrm/admin/scheduleReminders). Check if you can configure it there first? I've tried a scheduled reminder just now and see the expected email address when I receive it.

The "random set of letters" is a feature called Variable Envelope Reply Path ("VERP") which permits CiviCRM to better identify and track bounces, unsubscribes and other mail system errors by having them "return" to a unique, identifiable email address.

See also this question: How does Civimail reply tracking and forwarding work?