looks to be a type of smartweed.

Are the leaves thin like grass, or more thick/meaty? The pic is fuzzy for my bi-focaled eyes, but looks like some kind of 'fat grass,' but also resembles Commelina, or Tradescantia fluminensis. Adding a pic of a single stem could help.

The overall impression from the sparseness of the 'good grass' is that the area might be too shady for lawn grass to do well. If so, you could smother that whole area easily and make a mulched bed for part-shade plants.