If you want to remove the 'Theme settings' option from the affiliate panel menu and 'Themes' from 'My profile', you should follow this description:
At Merchant panel > Configuration > Design > Affiliate panel theme > click 'Edit theme' at the Active theme (if it claims to create a new 'Copy of...' theme, just click Yes), look up the file named "system_menu.tpl" and remove the following line:
{widget id="PanelSettings"}
Then if you want to remove 'Themes' item also from 'My profile' look up also the file named "myprofile.tpl" and remove the following line:
<td>{widget id="Themes"}</td>
or
{widget id="Themes"}
Save your modifications and make sure your freshly edited (and created) theme is set as default.
To make sure your affiliates use the theme you wanted to, click the "Set as default" button at any other theme and when the change is applied, then click again the "Set as default" button at the desired theme you want them to use. When the confirmation box pops up, make sure you tick the checkbox next to the "Apply also for existing affiliates".