Hi gjposton,
Welcome to Apple Support Communities. From my understanding, it sounds like you see blank space in the Mail app after email messages are deleted. I’d love to assist you.
For this issue, I recommend connecting to another reliable network to see if the issue persists. I see that your iPhone is connected via Personal Hotspot. Try turning Personal Hotspot off in the Settings app, then connecting to a reliable Wi-Fi network. It's possible that your device's connection is preventing Mail from updating as quickly as expected.
If the issue persists, I recommend taking steps 1-3 here: If an app unexpectedly quits, stops responding, or won’t open. Force quitting the Mail app, restarting your iPhone, and checking for updates can help resolve the issue.
Lastly, consider how your email is synced to your iPhone. Is it via a web email account, or are they synced with another device (i.e. iPad or Mac)? If so, check to see if the issue continues when deleting emails from your other device or from web mail.
I hope this information was useful. Kind regards.