In MapInfo, how can I remove polygons from a table according to whether or not points from another table fall within their boundaries?
You will need to use the SQL select tool which is found in the Query menu.
Below is a polygon layer and point layer.
In the SQL select tool, you'll have something that looks like this:
Ensure that your polygon layer comes first in the "from Tables:" field.
The results selected:
With the polygon layer editable and the results selected, just press DELETE. This can be done in either the map window or the browser window.
If your goal was to select polygons that didn't have a point inside them, then after you perform the above selection, go to the Query Menu, then "Invert Selection". Then delete.