Hey there Jsr4929,
Thank you for using the Apple Support Communities! We understand you're receiving feedback from recipients of your shared videos, that the quality is a bit blurry, yet things are clear on your end. Let's see if we can isolate this further to help.
Is this only occurring when sharing through the Messages app?
Are your devices both updated to the latest iOS? Update your iPhone, iPad, or iPod touch
If they restart their phone after receiving the video, does that help at all? Restart your iPhone
Are they connected to cellular data or Wi-Fi when viewing the video for playback?
Are the videos of a certain length? Or, are all videos affected?
Does it matter which video quality you're recording in: Record HD or 4K video with your iPhone or iPad. Or does it happen with both HD and 4K recorded videos?
We look forward to hearing back from you.
Best regards.