Hi Greg,
With level 2 the following process exist and if you could let me know in which step you are when you say "How do they remove it from Ariba and how is that communicated back to the supplier system?" in your initial comments
Step 1: End user accessed Ariba
Step 2: End user searches for item across catalog (from all suppliers) available within Ariba (as this is Level 2)
Step 3: Level 2 Punchout to supplier to validate current price and availability of selected item
Step 4: Completed shopping cart is brought back to Ariba
So if you see till the Step 3 is triggered everything happens in Ariba and users can edit local cart(Within Ariba) and all editing will still pass through Step 3 validation which is done by the Supplier site on Price and Item availability which is indirectly covers quantity validation also.
If my understanding is correct, before step 3 initiation you still have the delete option for end user in edit cart so there would not arise a situation where you send qty
Zero to vendor site to check availability.
If this isn't the case then "edit" POSR and set the quantity = 0 looks the only immediate option. Nevertheless thanks for asking this question and please update me on how you finally closed this.
Regards
Vilas