Business Links Act of 2003 - Amends part A (Temporary Assistance for Needy Families) (TANF) of title IV of the Social Security Act to replace bonus grants to reward high performance States with innovative business link partnership grants. Requires the Secretary of Health and Human Services and the Secretary of Labor, under such program, to jointly award grants to eligible applicants for programs to enable eligible individuals with limited English proficiency or other barriers to employment to: (1) increase their wages, especially by providing supports and services at or near work sites and to identify and strengthen career pathways by expanding and linking work and training opportunities for such individuals in collaboration with employers (to promote business linkages); or (2) provide for transitional jobs programs which combine publicly subsidized time-limited employment in the public or nonprofit private sector with skill development and activities to remove barriers to employment. Adds antidisplacement protections for workers.