Chelating agents and silica scale control additives are often employed separately in conjunction with performing a dissolution process in a subterranean formation containing a siliceous material. Carminic acid and related compounds may be used to perform similar functions dually in various subterranean treatment operations. Methods for treating a subterranean formation can comprise: providing a treatment fluid comprising a carrier fluid and an ortho-dihydroxylated aromatic compound comprising a substance selected from the group consisting of carminic acid, kermesic acid, any salt thereof, any derivative thereof, and any combination thereof; and introducing the treatment fluid into a subterranean formation.