Reply To: Remove "Search Results for:" box in the search results page

To remove the image overlay, add this CSS to Appearance > Customize > Additional CSS
Adjust as you like; you can use background-color: transparent;

.home-welcome {
    background-color: rgb(0, 0, 0);
    background-color: rgba(0, 0, 0, .4);
}
.home .search-bar {
    background-color: rgb(0, 0, 0);
    background-color: rgba(0, 0, 0, .4);
}

To adjust the padding on the Home Welcome section, add this to Additional CSS, and you will want to add some bottom padding:

@media only screen and (min-width: 767px) {
.home-welcome .wrap {
    padding: 150px 0 0 0;
}