If you are worried about legal compliance, then you really need to consult professional legal advice, rather than relying on advice posted on a forum.
That said - (and I am not a lawyer, so do NOT take this as legal advice) GPL means that anyone who gets a copy of the software must have the right to access the source code and modify it as they see fit (as long as they also follow the same rules of sharing the source code and allowing others to modify it). When someone logs into a Moodle server, they are not receiving a copy of the software (just the pages generated by that software), so there is no requirement to give the user of your site access to the source code. If you were to distribute a modified version of Moodle (for people to install on other servers), then you are also fine, as distributing Moodle includes all the source code and permission to modify and redistribute as they see fit (with the caveat that you cannot sell services using the Moodle trademark, without permission from Moodle HQ).
Again, that is my opinion on this - if you are worried then employ a lawyer to check.