These branches sprout out above the graft line.

That's impossible unless it's some type of chimera. Now a chimera could explain the seedless fruit. Is the Lime a Persian lime (seedless) or Mexican (Key / seeded) ?

The limes are seeded

You have one strange plant there. Maybe Dr. Manners can shed some light.

After doing some investigation, you are right that the branch stems from the bottom. I had a few of the branches confused since they wrap around each other. Here is a picture of the branch. Should I cut it off? It is a pretty large branch and I do not want to harm the tree. Thanks again! I have learned soo much about citrus trees by researching this

Normally, a branch from the rootstock is removed because it takes strength away from the rest of the tree. However, you may have something valuable there. A rootstock variety that doesn't produce seed is not common. It obviously has some trifolate in its parentage. The fact that it does not taste disgusting is surprising with trifolate parentage. It is probably some type of citrange like C-32 which doesn't produce much seed but it's not commonly used for a rootstock for that reason. It may be a useful cold hardy citrus variety. If it were my tree I think it would keep that branch a little longer until I found out a little more about it. It may be nothing special but who knows?

I completely agree with Tim. Don't cut it now. We must first truly understand what it is.