By "Software Inventory" do you mean just the Add/Remove Programs data, or all AeX SW * data classes? The easiest way would be to just delete the resource outright, then run a recreate full Inventory after updating configuration (it will show up as a new resource). Then run the regular Inventory jobs and it will re-populate the info you want.
Another way (which you need to test first!) if you can't or don't want to lose the rest of the inventory on the machine would be to export the computer by right-click --> Export, then save the .XML. Open the .XML file with Notepad++ or some other XML-aware editor (I like PrimalScript) and remove the sections for the dataclasses you're wanting to remove. Save the modified file with a new name. Then, delete the resource from the Console. After it finishes deleting, import the modified XML back in to the console. Note that with this method, you'll lose any collection memberships that computer might have been statically included in (since static collections are based on GUID, and you're removing that resource GUID from the console).