Nope! Tor is just for your privacy, the person receiving the transaction isn't actually aware of any information about you except your payment address. What this does do is when you make a transaction with your wallet, it is possible for node that you are broadcasting the transaction on to record your IP address. Tor will help hide that from the node by using Bitcoin nodes that route transactions only through Tor. Since Tor uses a network to obscure your IP address, no node is capable of knowing that information either.

But, because Bitcoin operates on both the internet and Tor, a transaction that originates from a Tor node can be safely and anonymously seen by all non Tor nodes as well.

So basically its just an extra step in order to prevent data tracking. Specifically associating transactions (and consequently Bitcoin itself) directly to an IP address of the person that made the transaction. The information isn't recorded on the Bitcoin network itself but can be collected in association with the Bitcoin network.

This is also why it does not matter if the other person is using Tor or not because Bitcoin does not use IP addresses to route transactions over the network. Transactions broadcast themselves to a node, and then that node broadcasts it to the list of nodes that are connected to it until the transaction is in everyone's mempool ready to be validated and mined into a block.

There would be at most minimal negative impact because sometimes the connection to Tor fails but that isn't a big deal since the connection can be tried again. This can potentially cause the transaction to fail but cannot cause a loss of funds on Bitcoin network. Either the Bitcoin moves where it should or it stays put, no in between.