Look-back Elimination Act of 2013 - Amends part E (Foster Care and Adoption Assistance) of title IV of the Social Security Act (SSA) to eliminate the requirement that, to be eligible for foster care maintenance payments, a child would have been eligible for aid under the former Aid to Families with Dependent Children (AFDC) program (predecessor of the Temporary Assistance for Needy Families [TANF] program under part A of SSA title IV) at the time of removal from the home.

Expresses the sense of the Congress that: (1) the AFDC eligibility requirement for federal foster care and adoption assistance benefits should be eliminated and replaced with income eligibility standards that are based on modern, balanced criteria that treat all children equally; and (2) the Secretary of Health and Human Services (HHS) should collaborate with Members of Congress and child welfare advocates in developing any modification standards.