Military Widow's Tax Elimination Act of 2017 This bill repeals certain provisions which require the offset of amounts paid in dependency and indemnity compensation from Survivor Benefit Plan (SBP) annuities for the surviving spouses of former military personnel who are entitled to military retired pay or who would be entitled to such pay, except for being under 60 years of age. The Department of Defense is prohibited from recouping certain amounts previously paid to SBP recipients in the form of a retired pay refund. The bill requires (current law authorizes) the Secretary of the military department concerned to pay an annuity to a member's dependent children when there is no eligible surviving spouse. The Secretary concerned shall restore annuity eligibility to a surviving spouse who earlier agreed to transfer such eligibility to the surviving child or children of a member.