Code warranty (guarantee) is quite common in software development, although 6 weeks is a quite short period - from my experience 3 months warranty is more common. It basically means that any bug you find in that period will be fixed for free, after that period they can charge you for fixing the bug.
The best way to use this period is to get a good tester to test your site for the fixes they put in and to try to break what they have done. Anything you found within these 6 weeks in the area they were addressing should then be fixed for free.
In fact one should always insist for a clearly defined warranty period if they order software from a third party.