I got it worked by modifying several files :D (The functions.php modification didn’t really help.)
The key of the solution is to attach the API Key to the URI string. The files below are in enfold theme folder.
config-templatebuilder/avia-template-builder/assets/js/avia-element-behavior.js
framework/php/class-framework-widgets.php
js/shortcodes.js
In avia-element-behavior.js
line 55 (or somewhere else)
replace
maps.googleapis.com/maps/api/js?v=3.24&callback=av_builder_maps_loaded
by
maps.googleapis.com/maps/api/js?v=3.24&callback=av_builder_maps_loaded&key=xxx-xxx-xxx
In class-framework-widgets.php
line 1369 (or somewhere else)
replace
maps.googleapis.com/maps/api/js?v=3.24
by
maps.googleapis.com/maps/api/js?v=3.24&key=xxx-xxx-xxx
In shortcodes.js
line 458 (or somewhere else)
replace
maps.googleapis.com/maps/api/js?v=3.24&callback=aviaOnGoogleMapsLoaded
by
maps.googleapis.com/maps/api/js?v=3.24&callback=aviaOnGoogleMapsLoaded&key=xxx-xxx-xxx
Don’t blame if it doesn’t work on your site. :P