Cannot get rid of scroll bars despite leaving 'scroll long text' unchecked

I have created a form with text fields that must be completed by signers. For each of these fields, the properties are set up such that 'multi-line' is selected, but 'scroll long text' is NOT. I want signers to be limited in what they can type, so that they can only fill the box that is visible, with no scroll bars. However, whenever I test the form as a signer, the scroll bars appear and I can enter as many lines of text as I want. I tried setting a character limit, but the scroll bars remain. How do I get rid of those and have the features work as they're supposed to?