The City Clerk shall, at the time of certifying other city taxes to the County Clerk, certify the unpaid costs for removal of snow or ice performed under the authority of § 13-504 and the County Clerk shall extend the same on the tax roll of the county against the lot or parcel of ground. The cost of such work shall be paid from the General Fund or other proper fund of the city, and such fund shall be reimbursed when payments therefor are received or when such assessments are collected and received by the city.