I figured this plugin will never get an update supporting the mobile version, I took the liberty to add a simple fix/support for our mobile users.

Attached is the mobile support folder, unzip it inside your "glconnect" plugin folder.

Follow the steps below:
1- Log in to your cPanel.
2- Locate the folder "ow_plugins".
3- Open the folder "glconnect".
4- unzip the "mobile.zip".
Voila!

Place this code in your "base.css" mobile theme folder.
"/ow_themes/[your theme]/mobile/base.css"

/** GOOGLE RECODE MOBILE CSS FIX **/
.glconnect_button {
    height: 21px;
    display: inline-block;
    cursor: pointer;
    border-bottom: 1px solid #8d2d1d;
    vertical-align: top;
    margin-left: 10px;
}

span.glconnect_button_text {
    padding: 0px 7px 0px 29px;
    color: #fff;
    text-decoration: none;
    font-size: 12px;
    line-height: 20px;
}

span.owm_btn_g_text {
    font-size: 18px !important;
}

.owm_btn_g {
   width: 95%;
}

P.S Any future updates by the plugin will override the changes.

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100% Operational. To be safe, test it first before putting it on a live website.
1.7.x
1.8.x
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See Below