https://developer.salesforce.com/docs/atlas.en-us.api_meta.meta/api_meta/meta_appmenu.htm
It should be under "AppMenu" metadata ("Salesforce1.appMenu"). You should be able to pull the changes and push the changes through metadata with the following structure:
<AppMenu xmlns="http://soap.sforce.com/2006/04/metadata">
<appMenuItems>
<name>MyDay</name>
<type>StandardAppMenuItem</type>
</appMenuItems>
<appMenuItems>
<name>Tasks</name>
<type>StandardAppMenuItem</type>
</appMenuItems>
<appMenuItems>
<name>Feed</name>
<type>StandardAppMenuItem</type>
</appMenuItems>
<appMenuItems>
<name>Dashboards</name>
<type>StandardAppMenuItem</type>
</appMenuItems>
<appMenuItems>
<name>Search</name>
<type>StandardAppMenuItem</type>
</appMenuItems>
<appMenuItems>
<name>Events</name>
<type>StandardAppMenuItem</type>
</appMenuItems>
<appMenuItems>
<name>DE_Widget</name>
<type>CustomTab</type>
</appMenuItems>
</AppMenu>