the good news is that it is possible to turn off the "available" tag at the top of the quiz. However, it is not a setting on the HotPot activity settings page so you might have to delve into the code a little to achive your goal.
In the short term, the quickest way to remove the message is to edit the script that adds it.
- open "moodle/mod/hotpot/view.php" with a text editor
- change the following line (about line 132) ...
$available_msg = get_string("quizavailable", "quiz", userdate($hotpot->timeclose))."<BR>\n";
... to this (add two backslashes to the start of the line) ...
// $available_msg = get_string("quizavailable", "quiz", userdate($hotpot->timeclose))."<BR>\n";
- save the file and close the text editor
The two backslashes tell PHP to ignore the line, so the message will not be set.
Perhaps what you really wish to do is to remove the finish date completely? Certainly, I want to do that sometimes. That would require modifying the HotPot activity settings page so that the Open and Close dates for the quiz could be left unset. I will add this to the list of tweaks to add when time permits.