LOL, I had a support request on this one too. They just log the value they get, nothing is done based on it, according to support.
On the "network advertises [higher/lower] mtu: XXXX" logs, they did suggest:
Changing TCP MSS is only half solution and it does work for other protocols, so anyway there should not be a blackhole router in the packet path which does not send or drop other router ICMP notifications about to big packets.
We are not aware of providers which do not actually supports MTU of 1500, but they recommend lowering MTU because:
each subscriber connection from the tower to the packet core is tunneled using GTP tunnels using the transport network
optionally GTP tunnels may be encrypted using IPsec
transport networks may be built using same MTU as 1500
so when clients sent packets bigger than the transport network MTU minus GTP and encryption headers then this packet must be split into two packets in the transport network which slightly increases the data amount but doubles the processing amount on the transport network/devices.
So does " doubles the processing amount on the transport network/device" make a difference in real world is still an open question. But MT suggest PMTUD detection should work through an LTE network, so higher MTU may not be a problem. I historically just set the MTU match these logs message (which also match the MTU the carrier documents, AT&T in US in my case ). But also seen larger MTU's accepted than the value reported in the log messages.
So I suspect the value reported MAY be the lowest supported by the carrier's overall network, but maybe higher on some paths. But dunno.