Rounded border is one of the common requirement when working with table in adobe forms.
Step 1: Add table as per your requirement.

Step 2: Select table, and go to Border palette.

Step 3: Select Corners from four available.

I'm shocked after seeing this odd behavior.
Then i come to know that, that extra border is of in Textbox's border.
Step 4: Select textbox (ex. Header1). Select Edges as Edit Individually and Style as none for top and right borders.

Step 5: Do for all corner boxes, and see the preview.

Hope this helps.
Step 1: Add table as per your requirement.

Step 2: Select table, and go to Border palette.

Step 3: Select Corners from four available.

I'm shocked after seeing this odd behavior.
Then i come to know that, that extra border is of in Textbox's border.
Step 4: Select textbox (ex. Header1). Select Edges as Edit Individually and Style as none for top and right borders.

Step 5: Do for all corner boxes, and see the preview.

Hope this helps.