Hello Wightrabbit.
Thank you for using Apple Support Communities and for sharing these details with us. The white line indicates where the bottom of the screen is so you can swipe to exit apps for example. As you mentioned, this white line does fade away after a few moments. However, it sounds like the white line isn't fading away while using a specific third-party app. If so, we'd like to help out. First, try restarting your iPhone and also force close the third-party app to see if that helps:
Restart your iPhone - Apple Support
1.) Press and hold either volume button and the side button until the power-off slider appears.
2.) Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
3.) To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo.
Close an app on your iPhone or iPod touch - Apple Support
1.) From the Home Screen, swipe up from the bottom of the screen and pause in the middle of the screen.
2.) Swipe right or left to find the app that you want to close.
3.) Swipe up on the app's preview to close the app.
If these two steps don't resolve your issue, you can try to uninstall and reinstall the third-party app: Delete apps on your iPhone, iPad, and iPod touch - Apple Support
Also, install any pending updates that might be available for your iPhone. This can sometimes resolve various issues: Update your iPhone, iPad, or iPod touch - Apple Support
1.) Back up your device using iCloud or your computer.
2.) Plug your device into power and connect to the internet with Wi-Fi.
3.) Go to Settings > General, then tap Software Update.
4.) If you see two software update options available, choose the one that you want to install.
5.) Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do.
We hope this information is helpful. Cheers.