[Edited 02/15/2018 @ 1:05 PM PT]
If the payments are actually contributions to a qualified Health Reimbursement Arrangement, they are not taxable income and you do not have to report them on your return.
The Health Reimbursement Arrangement must comply with the requirements outlined in IRS Pub 502: Health reimbursement arrangement (HRA) and may also apply to retirees. Your former employer can tell you if this is an HRA plan.
(If you are receiving informal payments or reimbursements for medical expenses from a current or former employer, they are most likely taxable in the year received. If the employer is making informal payments to you (not reported on a Form 1099-MISC), you can report this income on Line 21, Form 1040 using the "Other Reportable Income" interview - for the Description, enter "Medical expense benefit".
Go to the Other Reportable Income interview, the very last interview in Wages and Income (Federal Taxes tab > Wages & Income category > Less Common Income subcategory > Miscellaneous Income sub-subcategory). Or enter "other reportable income" in the Search Box and select "jump to other reportable income". These payments are NOT wages).