For the love of all that is holy, do not do this. Consider:
Alice wants to send you 1 bitcoin. She asks her wallet provider to send you 1 bitcoin. Her wallet provider sends you the bitcoins it got from Bob when he deposited into his wallet.
You look at the transaction and see that the coins came from Bob's deposit address. So you send coins back to that address. Alice's wallet provider sees coins received to Bob's deposit address and credits Bob.
Bob wonders why he received some bitcoins from a random stranger, but since he has no idea who you are and no way to contact you, he just keeps them. Heck, maybe it's an address he made public as a tip jar and he has no reason not to think it's a tip.
Alice might eventually wonder why she didn't get her bitcoins. If she contacts you, you'll give her the transaction ID. She'll think, "Hmm, that's not my address. But it must belong to my wallet provider. So they must have the bitcoins. When I explain to them that they're mine, they should credit them to me."
And now we have a massive mess where everyone is blaming everyone else and Alice thinks her wallet provider stole from her and you think it wasn't your fault. But you're wrong.
Please do not do this. It does not make any sense. (The story above is real. Only the names have been changed to protect the innocent ... and the guilty.)