Ms Elachi was impeached on September 6 while the EACC issued the summonses on Tuesday.
The MCAs want the High Court to temporarily quash the summonses and the anti-graft body barred from investigating them.
The ward representatives did not honour the commission's summonses on Wednesday, Majority Leader Abdi Guyo saying they will appear after their retreat in Mombasa County.
Mr Guyo noted that they will face the EACC investigators but that they will not nbow to intimidation.
Those summoned include Mr Guyo, Minority Leader and Kileleshwa MCA Elias Otieno, Minority Whip Peter Imwatok, Waithaka MCA Anthony Kiragu who moved the impeachment motion, Ngando's Peter Wahinya and Nominated MCA Mary Njambi.
Others are Leah Supuko, Doris Ngoyo, Ruth Mainigi, Nancy Maole, Grace Muthami, Susan Kavaya and Laura Mwololo.