The branch router should advertise the local LAN with the EIGRP network command and make the LAN- facing interface passive. A passive interface allows the connected network to be included in EIGRP advertisements while suppressing EIGRP hello packets and neighbor formation on that interface. This is exactly what the engineer needs: remote EIGRP neighbors learn the LAN subnet, but unnecessary multicast EIGRP messages are not sent onto the user LAN where no EIGRP neighbors should exist. Replacing EIGRP with a static default route would not meet the requirement to advertise the local LAN through EIGRP.
Redistributing connected routes can work, but it is less clean for a simple LAN interface and can introduce external-route behavior or policy complexity. Advertising the subnet as a stub network does not suppress multicast hellos on the LAN interface by itself. Cisco design best practice is to use passive interfaces on LAN- facing interfaces that should be advertised but should not form routing adjacencies. Reference topics: EIGRP passive interface, network statements, branch routing, unnecessary neighbor prevention, multicast control traffic.