There is no way to use contextual links on mobile devices at the moment, because they are only triggered by hovering your mouse over the editable/configurable items, and mobile devices work with taps.

In D8, they have added an "Edit" button at the far right of the admin bar, that toggles contextual links on/off:

screen shot 2018-12-11 at 1 48 12 am

We should have the same.

GitHub Issue #: