In addition to the powers of said district and of the trustees thereof as originally vested, such enlarged district and the trustees thereof shall have power and jurisdiction to provide and maintain adequate and suitable sewerage systems for the entire district; to provide and maintain sewage disposal or reduction plants; to enter upon any street, alley or public place in any municipality, city or village, within the limits of such enlarged district for the laying of sewers and the construction of sewerage systems. The district shall pay to such municipality, city or village, upon claim being filed therefor, the amount of any damage to any pavement or any public improvement. Such municipality, city or village shall not be entitled to any compensation for the use of its streets, alleys or public places except for damage to such public improvements.