update

src/sass/gtk/apps/_lightdm.scss

@@ -50,6 +50,19 @@
 
   // the entries, one for the username, one for the password
   entry {}
+
+  GtkComboBox {
+    background: none;
+
+    .button {
+      &, &:hover, &:active, &:focus {
+        padding: 0;
+        background: none;
+        border-style: none;
+        box-shadow: none;
+      }
+    }
+  }
 }
 
 // the buttons, alternatively this could also be done with a simple ".lightdm-gtk-greeter button"