When playing around with carpets I noticed that when they where placed on a Dead Bush or Grass they completely deleted the block and all potential items to come from it. I tested it on a flower and it did not delete the flower.
Replicate
Get some Carpets
Find Dead Bush or Grass
Place carpets on Dead Bush and Grass (Preferably on a few to see that it negates the item drops as well)
This is the case for all blocks; grass and dead bushes (along some other blocks, such as snow or vines) are blocks that can be replaced by right-clicking onto them with a block.