It's hard to identify with certainty from the photo, but this is most likely Mock Strawberry, a very common lawn and garden bed weed that is found throughout the state, though isn't currently listed as invasive despite being non-native. Given its vigor and aggressiveness, it probably will rebound just fine if temporarily damaged by dog urine (as most perennial plants would), though it is not noted as being evergreen, so would likely lose its leaves during winter (as would the clover, if it matters, which is also non-native). It can be very hard to remove manually, because it roots at the nodes (where leaves attach to the stems) as it runs.

Miri