10
My thoughts are that you should, on your PC, edit this file:
xoops_root/modules/system/templates/blocks/system_block_login.html
Remove these three lines of code:
<a href="<{$xoops_url}>/user.php#lost"><{$block.lang_lostpass}>a>
<br /><br />
<a href="<{$xoops_url}>/register.php"><{$block.lang_registernow}>a>
Then, in this order:
1. Login to your website and set "Check templates for modifications?" to "Yes"
2. use your FTP client to rename the original template file to system_block_login.old
3. upload the newly modified system_block_login.html
4. go to your homepage and refresh it
5. set "Check templates for modifications?" to "No"
6. use your FTP client to rename register.php to register.old
7. set "Enable registrations" to "Yes"
If it were me I'd either replace the three lines of deleted code in system_block_login.html with some text saying who to contact for a registration or make a custom block saying the same thing.