Sure, I think. Can't you set the line color for the field to null (that is nothing) and accomplish what you want?
Ron Smith, MD, 'The Pediatric Guide For Parents'
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The is no formatting feature to remove the box from the x mark in a checkbox formatted field.
However, I frequently create a related table and the table will have two fields, the X and a container field. In the container field, I put a nicely formatted graphic "X" or checkmark or whatever I want (e.g., you can make it in Photoshop or copy one from the internet). I make the field a normal edit field that is a button that toggles the X on and off in my primary table, but displays the container field in the related table. That is how I make ugly FileMaker checkboxes look much more professional.
You can download the following example file.
If you're background is straight forward...white or solid color (not a gradient), you can put a 2 pixel see through square over the field to hide the check box outline on the layout/printed report.
Hope that helps.
While I don't know how you are using the data collected by the checkbox, here is an idea. On your input layout, just use a checkbox whose value list is a single "X". Then you could place that field on your other layouts using a nicely stylized font and not use the checkbox at all.
I mentioned the related table checkbox earlier. But one thing I see some people do is put a checkbox on a layout and a conditional text box with ony a space on it over the checkbox and set it to conditionally go white to cover up the checkbox when you are turning it off and to turn transparent when you want the check box. You make this text box a button to alternate changing the field to "X" and off. That way you accomplish the same thing without another relationship.
Here is an easy solution to your problem, if you haven't found one already.
In Layout mode, Select the field with the checkbox set,
In the Inspector under the Appearance tab, set the line to Solid, 1 pt and (here is the trick) in the line color picker next to pt size set the color to the first option in the upper left. It looks like a white box with a diagonal red line through it. Once selected it will look like a diagonally split box with black on top and white on bottom.
Save the layout and, if it works like mine, no boxes will print out for the checkboxes, just an X for the ones that match our value list item.
Hope this helps,