So, I have a leaky faucet. I am in the process of disconnecting everything so that I can take the faucet out and inspect what's going on with the leaky faucet. However, when disconnecting the faucet, I encountered a t-valve that I don't recognize (picture below) and am not entirely sure how to disconnect the hose without damaging it. This is connected to the hot water, and to the dishwasher. I have disconnected the cold water without issue.
Both of these hoses run all the way into the faucet, there is no other section to disconnect them from.
My primary inclination would be to just yank, but I don't want to attempt that without first figuring out if it's a bad idea, or if I shouldn't be worrying about it since I might wind up having to replace all of the hoses anyhow.