lotlog

No, I did not use any plugins on rewrite URLs. (or I don’t know if there is a plugin make it happened.)
Here is the list of my plugins:

All In One WP Security
Google Analytics by Yoast
Page Builder by SiteOrigin
Wordfence Security
WPtouch Mobile Plugin
Vantage Theme

Instead of checking them one by one, I’d rather rebuild a wordpress somewhere else to see if any of these plugins leads to this situation.
I’ll make it tomorrow.

Found that if I choose a custom icon as the page icon, WPtouch will change the path from
https://example.com/wp-content/wptouch-data/icons/custom/example.png
into
https://example.com//example.com/wp-content/wptouch-data/icons/custom/example.png
which leads to your situation.