I've seen a few plugins that allow you to read this data, but nothing to write/remove it.
I know in Android there is a way to do this with the support lib (https://developer.android.com/reference/android/support/media/ExifInterface.html#saveAttributes())
And there appears to be several examples for Modifying EXIF data on iOS.
But I don't see this in any image or standalone plugins that handle this for flutter.
This all seems a bit strange, since there are several example Flutter Photo Sharing apps using Firebase storage and such. But none, that I've seen, are removing any of this data.