Hi, Mike! Welcome to iPF!
Afaik there's no way in the Settings app to change this behaviour.
You could try to delete the email account that's moving incoming emails to trash, and set it up again. I suppose this won't change it's behaviour, though.
You'll have to change this in the email account through a browser. Go to the account's settings there and take a look at them. Maybe you'll have to keep emails on the server.