This appears to be Spotted knapweed (Centaurea maculosa), an invasive plant on particularly unfertile, dry soils across Michigan and other states. Spotted knapweed is a biennial to short-lived perennial in the Aster family capable of producing one thousand seeds per plant. Stems are erect, wiry, and rough to slightly woolly-hairy. Leaves are grayish green and dissected with many deep lobes. Flowers are pink to purple.

Along with the ability to compete well with native vegetation, there is evidence that spotted knapweed releases chemical substances that can inhibit the growth of surrounding vegetation (allelopathy). High concentrations of these chemicals are reported to inhibit the germination and growth of grass and conifer seedlings. Allelopathy is not, however, thought to be the major factor in the competitiveness of spotted knapweed. Rather, the aggressiveness is attributed to prolific seed production, rapid seedling establishment, and depletion of soil nutrients.

I would spot-treat with glyphosate and then replant with grass seed.