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:

We should have the same.
GitHub Issue #:
3417
Recent comments
Hi Editing I see this: The CSS looks like this: /* Level 1: Standard Numbers */ .field-name-body ol { list-style-type: decimal; } /* Level 2: Lowercase Letters */ .field...
Numbered List format is different when editing
Done: https://github.com/backdrop/backdrop-issues/issues/7097 Feel free to edit it with better technical language. I'll have ago at vaccinating it but I'm only a user and the...
Numbered List format is different when editing
Hi Mike. That looks like a bug. The CKE ordered lists when editing have the correct CSS to format those lists correctly, but when Backdrop displays the body field in Basis, it doesn't...
Numbered List format is different when editing