Whenever it shall appear to the legislative body that payments have been made on any such assessments or bonds prior to the reassessment, it shall be its duty to cause to be published in the newspaper in which the ordinance or resolution of intention for the work was published, unless the legislative body directs publication in some other paper, a notice stating the fact of such reassessment and calling upon all property owners affected by the work to make claim for refund within two years from date of the first publication of the notice. Reference shall be made to the reassessment and diagram for all particulars. Such notice shall be published once a week for two weeks.