Pete I work in this industry for an independent funeral home. State laws do not require funeral homes to take finger prints . You can ask if they would and as a courtesy they could . The markers in most cemetery are covered by a fee you may have paid called endowment care or perpetual care for the marker it’s self. This is for damage repair or replacement and to raise it when it sinks down. Just tell them. When you visit look at the markers around the cemetery ? Are they neglected ,broken or sunk down, Does class action suite come to mind?