It looks like miner's lettuce, one of the claytonias. If I'm correct, you can get rid of it by eating it. It's a lettuce substitute and is considered a delicacy.

It self-sows pretty happily, so don't let it go to seed, or try to smother it somehow. Maureen

Nope, not miner's lettuce. Googled it. Looks similar, but plant I have grows much different. More viney with double leaves at junctions. Plus miner's lettuce is in cool areas of the west. I'm in central Fla.

I have my doubts if this is what your dogs are bringing in. It lacks the fuzz on the stems to tangle in coat nor are the seeds large enough to attach to coat.

It is a weed but a very pretty weed. Has bright blue flowers in early spring. From a distance looks like someone has wiped their brush on the ground.

I am also in central Florida and I'm pretty sure that this is Heartleaf Drymary also known as West Indian Chickweed.