I bought the entire linkage kit. BTO strongly recommends replacing the spring behind the TV valve with the one that comes with the kit as the spring pressure is supposedly built into the geometry with the rest of the kit...

I'm not sure I'd absolutely insist on using the BTO spring in the VB, tho in some cases, it may be needed. Fact is the only difference in the BTO spring and a stock spring is the length...the BTO spring is slightly longer than most stock 700 springs. The stock springs in Corvette/Camaro/Fireturd 700s are the same length. There are also shims that can be used to do the same thing. Most(not all) "Shift Kits" have an optional spring for the TV that is marginally longer, and a weeeee bit stouter. There are also several different diameter valves that the TV linkage works against, and changing the spring also changes the working pressure of the valve, in some cases causing late/early shifts no matter how you adjust the cable.
Then again, the cost of the BTO spring is not outrageous, so that's not really an issue, and you can change the springs out without removing the valve body. I've never used the BTO spring in the VB, so I can't really say for sure what the difference might be, operationally. On the ones I've used the carb adapters on, they worked just fine without the BTO spring. I guess they are just really covering their bo-bos, in case some goober burns his new trans up using their kits. The longer spring will help the trans tolerate a mis-adjusted cable mo better.