You have the option to remove the video play-bar on your videos.
Videos uploaded to your Thinkific site are hosted with Wistia. Unfortunately, due to limitations of iOS, when a video is viewed in fullscreen, mobile devices do not allow you to use the Wistia video player and instead use their own native native mobile player which will display a play-bar.
Wistia also has more details on this functionality here: Inline Playback for mobile roll out
We understand that this is not ideal in some cases, and if you have any feedback on this, please don't hesitate to reach out to the Support Team.