If removing this old tubing from the furnace and from wherever it runs through seems to be a problem (tubing inaccessible, stack inside the furnace assembly, ductwork, etc.) I wouldn’t touch it at all. Disconnect the old tubing from the pump and cut the exposed sections shorter to get them out of your way (condensate pump and sump pump ends), purchase some new tubing and run it different way, so it is accessible for servicing and you can see any possible clogs inside of it.
However, since I don’t know your installation details / positioning of the furnace and other surrounding it items, I’m not sure if this will be easy / possible to install. Also, since the tubing is discharging condensate and there’s still leakage from underneath the furnace / air handler there might be another problem. Since your unit is older (as old as the townhouse?) there might be an internal problem / corroded / overflowing condensate pan located directly inside the “A” coil.
Coil’s location depends on the configuration of your system… so it might be above / below the furnace if mounted vertically or on its side in horizontal installations. PVC tubing that runs into the condensate pump is connected to that tray / pan so you’d have to get access to the compartment and check its condition.
Let me know if you have any other questions, just click “comment” below.