Login to administration->Real Estates->Fields->Edit ‘Purpose’->On all langauges remove wanted values, for example “sale” and “rent and sale” but one should stay or you can expect issues!

If you want just hide it, this can be done via css file templates\bootstrap2-responsive\assets\css\styles.css, add:

ul#search_option_4 li{
    display:none;
}

ul#search_option_4 li.list-property-button
{
    display:inline;
}

If you want to hide “All” in standard real estate bootstrap2-responsive template: