Hi Ruth,
I actually just finished resolving this issue for myself. I assume you are referring to the third-party MyCourses block and not the standard Course block. Removing the 'Enrol in another course' link is possible but only through editing the code manually, not through any setting/option available through the interface. Luckily, in case your not a coding whiz, the modification is a very simple one. If you navigate to the directory containing the files that determine how the block is generated (should be /moodlehome/blocks/myCourse/HTML_TreeMenu-1.2.0) there will be a file there called TreeMenu.php. Open this file and make the following changes:
on line 659, you can either comment out or delete this line all together, it is simply retrieving the string to display as the link.
on line 660, the link code is appended to the $html var which gets printed as content. You can remove the link by deleting the link and center tags which look like this:
<center><a href=\"CFG->wwwroot course \">$enrol</a></center>be sure not to delete the quote and semicolon at the end of the line which closes the string to be appended to $html
This will remove the 'Enrol in another course link'