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
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Hi Kevin I am interested assisting you developing a theme by cloning feature from existing WordPress website. Please let me know your suitable time to discuss further...
Create a theme from existing website
I've updated the Zulip link in both places I found it. No need to post again, unless you have something new to say. We'll pull together feedback from all the sources.
Backdrop CMS Core Priorities
Should we post here again, what we posted over there? Or would that unnecessarily duplicate things? The link to a Zulip thread in this initial post leads to an internal one, but there's...
Backdrop CMS Core Priorities