How to remove contents type drupal advanced search page
Advanced Search field can be disabled in Permissions settings (it should be disabled by default).


If you rather want to leave Advanced Search, but limit to specific content types, you can 1) Use Custom Search module, as advised by @Lance or 2) Dig through modules\search\*.* directory to see which function controls the content type of the Advanced Search options, after which you can use your own module to override the settings.