Now we're not talking about making your lye solution with brewed tea, I'm talking about using the actual tea leaves.
So what's the problem?
Imagine brewing yourself a cup of tea. You drop the tea bag into your hot water - what happens? The oils and essence from the herbs seep into the water giving it flavor, scent and (most importantly in this case) color. The same can happen in your soap. Depending on the plant used, you can get a sort of "halo" effect - bleeding - of the tea into the rest of the soap. If this is the effect you want - it's not bad looking - great! If not, you need to "prepare" your botanicals before putting them into the soap.
Preventing Botanical Bleed
The easiest way to prevent the botanical bleed is to basically make some tea. Make some tea with the botanical - letting it steep quite a while in very hot water. All of the color and oils that would have seeped into your soap will seep instead into your tea cup. Then squeeze the tea leaves well, and use them as you would have in your soap.
Doesn't that remove all of the good stuff from the tea leaves?
Well...yes, and no. If you are just using the tea for visual effect and/or light exfoliation, then no - the tea will look just as great in the soap, and be just as scrubby. If you want or are promoting any "healing" qualities of the tea (though I would argue that there are any left after the saponification is done), then no, you'll want to use the tea without steeping it first.
Not every botanical will give this bleeding effect - mints seem to be the worst, lavender a little, chamomile not so much. You'll just have to experiment with your particular combination of soap colorant, soap recipe and botanical additive. Have fun!