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()
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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.
You can use flutter_image_compress to strip the Exif (you can optionally maintain it). But I could not find any solution to edit Exif with Flutter.