Just to make sure I understand: did you build the circuit yourself, or did you buy a DIY kit from us? The part we used is 24AA02E48 — a small SOT23-5 part. We call it the MAC address chip, because it has pre-flashed globally unique MAC address. But you are right that it is an EEPROM.
If removing the EEPROM works, you can just leave it off. The only purpose of this EEPROM is to provide a real MAC address. The firmware is designed such that if this chip doesn’t exist, it will use software defined MAC.