Though Papaya and its seeds are good parasite inhibitors, they arent strong enough to knock out parasites by themselves. You can benefit from them by incorporating them with other anti- parasite things for more effect.
Those seeds you are passing could very well be Dog Tapeworm segments. I have these too and read from a link on someone's post here that dog Tapeworm causes these in the stools. They look like whole pumpkin seeds. You can get dog Tapeworm from only being bitten by a flea in your backyard--that's how easy it is to pick up this tapeworm. They are small tapeworms- thank Goodness!
Everytime I do a Colon Cleanse I see these "pumpkin seeds" in my stools. I think this is one good excuse to keep the colon clean-- these are better out than in.