I've never used Electrum on Android, so I'm not sure if it has a console to enter this.
As far as I'm aware, there isn't a way to increase the gap limit on the android version as there is no console
Question: Is there any way I can fetch that change address to the offline smartphone so I can export it's private key?
Another way that I can think of to get your private key would require that you use the seed and something like the Electrum Seed Tester:
https://github.com/FarCanary/ElectrumSeedTesterYou just need the "standalone" .html file. Using that you could find the required change address and matching private key. The trick is how to do that in an "offline" manner. If you had an OTG cable for your offline smartphone, you could transfer it via a USB stick.
Or, alternatively, you could setup an offline PC and install the desktop version of Electrum, restore from your Electrum seed and then you'll be able to increase the gap limit and/or manually generate change addresses until you find the one you want.
Failing that, another (more expensive) option would be to go into the Electrum address list (receive tab, tap the address shown), then tap the "receive" button to change the filter to show "change" addresses, then select the last one in the list and select "use". Then send some coins to that address. It
might force the wallet to generate more addresses. NOTE: I can't test this method as there isn't a TestNet version of the Android wallet available, so I can't guarantee that it will actually work.