Maybe Program is within a layout container that has a border? If not, is Measure perhaps a parameter and not a quick filter? Last thing, did you try removing Program and adding it again?
Also, did you mean to say 'neither of them have a border" ?
"I have a dashboard with two filters. As you can see, "Program" has a border whereas "Measure" does not. Except they both are on the same dashboard and come from the same worksheet, and when I go into the Format Filters section of both the worksheet and the dashboard, neither of them have a filter. Is this a bug?"
It turned out when I deleted the filter and added it again, the border mysteriously disappeared. I guess it was a bug.