To remove only specific categories from a list, can use a CSS trick, Attribute

Tutorial: https://css-tricks.com/almanac/selectors/a/attribute/

Apply this formula to theme search value you want to remove.

Ex: To remove “Sold” from this dropdown

 

 

Css Used:

.filter_menu [data-value="sold"] {
display: none!important;
}

And should apply in header search and half map search

Help to add custom css – http://help.wpresidence.net/article/how-to-add-custom-css/

Please remember to clear cache to see results. Help http://help.wpresidence.net/article/enable-or-disable-wp-residence-cache/