Keep asking a few more times. Several people have got the same “irresponsible” reply as you, but some others were lucky, as the following guy (he got an update for his H81M-H).
If GIGABYTE eSupport is still of no use, you can try to flash the BIOS with TPM2 support on your board using a hardware programmer (e.g. CH341A). Given the model of the boards are the same (just different revision), I think the success rate is quite high.