Here is a possible solution -
in /common_files/single/menu_box.tpl
Replace the text headers
{$lng.lbl_orders}
with a graphic - link similar to this :
<img src="{$SkinDir}/modules/TXS_Service_Scripts/images/admin-logo-box.png" alt="TheXCartStore"/>
I noticed that after adding add ons from TheXcartstore.com that their menu, which has a graphic at the top, opens fine when clicked on an ipad or iphone in 4.4.2
Change the image location to your own - just watch the widths so that it still fits on one screen.
Hope this helps