Quickly shut off the water to the fridge and then jumped on AppliancePartsPros. Found the exact part I needed and watched the video.
I was thrown a bit of a curve when I found the line from the filter was fixed directly to the intake valve.
On one of the forums, though, someone explained you can simply disconnect the old housing from the lines in the fridge, take the lines out of the new part, and install the new part.
Easy fix!