This is not possible with WMS. WMS gives you an image representation of the data. WFS gives the data itself (READ only), and WFS-T is a transactional extension of WFS that allows you to CREATE/UPDATE/DELETE data through the WFS protocol. In your case, for what you need, you can't use WMS / GetFeatureInfo but you need WFS-T or to use a different approach like JDBC to edit the content of your postgis tables.