If you are using WPML and you have a theme which customize strings are not detected you can use the fallowing code, you might need to modify it for your use case:

if (function_exists ( 'icl_register_string' )) {
    echo icl_translate('Theme Mod', 'text_in_wpml', get_theme_mod( 'theme_mod_name' ));
}

This basically register the string as it echo it.

And yeah – this will require you to have the strings translation plugin.