Set the RadGalleryElement.DropDownSizingMode property to Telerik.WinControls.UI.SizingMode.None. however, you will notice that when the gallery's popup is opened, the grip is visible. Please refer to the attached project.

Workaround:

Sub New()
    
    InitializeComponent()

    AddHandler Me.RadGalleryElement1.DropDownOpened, AddressOf DropDownOpened

End Sub

Private Sub DropDownOpened(sender As Object, e As EventArgs)
    Me.RadGalleryElement1.GalleryPopupElement.SizingGrip.SizingMode = Telerik.WinControls.UI.SizingMode.None
End Sub