There is no setting in Mendix Studio Pro to do that, so your only option (possibly) is to modify the styling client-side. Inspect button Search and button Reset.
In theme\styles\web\sass\app\_customs.scss add an entry
.mx-grid-search-controls {
display: none;
}
That might hide the search and reset.
There is another way to achieve that. See this post: https://forum.mendix.com/link/space/widgets/questions/101709