It could be dollar weed - check it against this picture. If still in doubt take a leaf and show it to your local nursery.

I can't tell much from the picture but it might be wild ginger. Can you get a better closeup and describe the shape of the leaves? Do they have round edges or scalloped? What is the growth pattern...single leaves off of runners? How big are the runners...wild ginger has thicker stems than most of the creepers like creeping charlie

Thanks for taking a look! The edges are smooth, and the leaves are almost heart-shaped when flattened. I'm heading to the nursery to see if they can figure it out!

The verdict is dichondra. Guess I'm not supposed to rip it out after all!

It is nice to know you do not have a yard full of weeds!