Should I remove this ?

[All Your Greens]

In the UK I would advise pinching out the side shoots on vine tomatoes. You can tell them as they grow 45 degrees between a leaf shoot and the main stem. This diverts plant energy in to growing the fruit and not growing excess foliage. It also means that fruit will start to develop earlier and ripen quicker.

I notice that much of the disagreement on this tread is between those who live in the USA and those who live in the UK. I probably wouldn't bother pruning if I had the weather of Texas!

Never prune determinate or bush tomatoes. This will defiantly reduce the yield.