another grape question

If your grape is a grafted variety, and these suckers (plants coming from the roots.. that's what these 'babies' are) are below the graft, you need to remove them.
Even if your grape isn't grafted, you want to establish a long single rod or stem in the first season, so prune them off anyway.
In future years, once your grape is well established, you should prune off the old growth once it has fruited.
Basically grapes are produced on rods of one year old wood, so the pruning method to use is to ensure you always have pieces that are one year old. You need to read an article about pruning to choose the method best suited to the way you want to grow your vine.

this red flameless(i think) is at least 1 one old at least I've had it for one year. I bought it at a popular all in one pharmacy and thought I'd give it a go. so last year I repotted it and watch it grow along with thousands of these suckers coming up through the soil and i thought maybe it was something else that got deposited from birds or something else. So I repotted it again this year into a bigger planter and no site of the suckers but just last week low and behold they attacked so i took your advice and pulled them out and i also trimmed the new growth vines back a bit. When i firstr got the plant it appearred as one 10 in brown stem that started growing vine through the summer and I got one bunch of grapes but haven't seen anything this year> I 've been watering well and don't have bug problems as it is in a huge pot on a patio in the city. this means not many bees but with no flowers or buds to pollinate it they couldnt help anyway They also get at least7-8 hours of sun with temps in the 80s so all I can do is hope at this point?