"Saluting the Fallen" is one of the song titles featured on the official Team Fortress 2 Soundtrack, listed as track number 33.
Team Fortress 2 Soundtrack | Saluting the Fallen
This was added in the May 1, 2020 Patch as a tribute to Rick May (deceased this April 8, 2020) being the voice actor for the Soldier. Basically, this is a rendition of "Taps" (a bugle call played at military funerals by the US Armed Forces). The call can be heard at 0:26, preceded by four drum ruffles.
This track can be heard on the main menu since the patch, and for the whole month of May.
Pretty sure you got the idea that it was set for May for his surname.
:copyright: TF2 Official Wiki for all the info.
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