Now we're getting somewhere. That looks like Oxalis. Try chewing one. If sour, probably it is an Oxalis. Trifolium (clover) has a flavor that reminds me of grass. In mid-day full sun do the leaves droop (not wilt!), as in this photo?:
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you find any in flower (look in lawn adjacent to your Costus bed)? The flowers of Oxalis and Trifolium are easy to tell apart.
Here's a pamphlet about Oxalis in Florida:
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are distributed like seedlings, so from seeds falling there after you laid the gravel. Source is likely your lawn or your neighbor's lawn. Explore a bit in the crushed stone to see if the roots are little bitty seedling roots or what. Some Oxalis produce bulbils on their roots and when you pull out the root you are likely to leave the bulbils behind. The bulbils sprout new plants.
Here's what I do with seedling crops. I first wait for most of them to die. That is the fate of most seedlings. Or I would lightly rake the rocks with a gardening claw, taking care not to damage the Costus. Any seedlings that survive I would dig out using a gardening tool to ensure I get enough of the root that it does not come back.
To prevent future seedling crops, find and eradicate the source. If this is Oxalis, you can treat with the specific herbicide others have mentioned. But if you don't eradicate the source, it will return.
Are the Costus growing on top of the fabric, or did you puncture it for each plant?
You have a "stone mulch" there. If you decide you don't like it after all, now is the time to take it all out and replace it with an organic mulch. I like organic mulches in part because it is easy to add more right on top of a seedling crop like this and kill the seedlings. However, if cats messing in the flowerbed are a concern, the stone mulch should discourage them.
Hope this helps,
Una