Survivor Benefits Improvement Act of 2013

Survivor Benefits Improvement Act of 2013 - Allows dependency and indemnity compensation (DIC) paid through the Department of Veterans Affairs (VA) to the surviving spouses of veterans to be increased for months occurring during the five-year (under current law, two-year) period beginning on the date of entitlement.

Provides that the remarriage after age 55 of the surviving spouse of a veteran shall not bar the furnishing of VA DIC, health care, educational assistance, and housing loans.

Authorizes the Secretary of Veterans Affairs to provide, to any spina bifida-affected child of a veteran who served on active duty in Thailand beginning on January 9, 1962, and ending on May 7, 1975, and was exposed to a herbicide agent during such service, the same health care, vocational training and rehabilitation, and monetary allowance required to be paid to a similarly-affected child of a Vietnam veteran.

Directs the Secretary to carry out a two-year pilot program to assess the feasibility and advisability of providing grief counseling services for the surviving spouses of veterans who die while serving on active duty.