WPML only stores cookies that are important for it to function properly.

List of WPML Cookies:

• wp-wpml_current_language – Stores the current language. This cookie is enabled by default on sites that use the Language filtering for AJAX operations feature.
• wp-wpml_current_admin_language_{hash} – Stores the current WordPress administration area language.
• _icl_visitor_lang_js – Stores the redirected language. This cookie is enabled for all site visitors if you use the Browser language redirect feature.
• wpml_browser_redirect_test – Tests if cookies are enabled. This cookie is enabled for all site visitors if you use the Browser language redirect feature.