Hi,
After a lot of trial and error I found a way how to do this for iOS
In your app in Construct3 add a global variable to hold the URL string and a javascript line to read the URL that was used to launch your game:
Export your game as iOS project and open it in XCode
In the Info tab in XCode, add a URL type. For Indentifier use your app identifier in reverse domain name format, for example com.mydomain.myapp. For URL scheme use your app name, for example myapp.
Now comes the tricky part. I'm open to better suggestions because my solution involves adding some code manually, and I realise this is not ideal.
In CDVAppDelegate.m, in the function didFinishLaunchingWithOptions add this code (after the comment lines that are already there):
This code defines a NSURL object (named url) that holds the URL that was used to start the app. If url is not empty, the URL parameterstring (url.query) is added to the startpage string as parameterstring.
After building and installing on your device, you can now launch your app on your device using a URL with parameters, for example myapp://main?test=test123
Because the Construct3 code is now launched with the URL parameters, the javascript code can pick up this string and you can use it in your application. In the example above it is added to a global variable.