Follow Up:
The “Alternate Text” field is populated by the “Alternate Text” field from the wordpress media tool. However it does not get applied to the image, which is confusing.
After playing with the widget some more I figured out that the “Alternate Text” field is being applied to the LINK TAG alt attribute. Which was very unexpected due to the presentation in your form.
Either:
1) Your widget form is confusing
2) The alt text is being added to the wrong element
If #1 is the case I would recommend having the “Alternate Text” field listed after the “Link” field and change the name to “Link Alternate Text”
