The reddish sawdust is frass, the excrement of larvae feeding under the bark. Several insects and borers cause frass but because of the reddish color, I suspect that is from the linden bark borer moth the larvae of which produce large amounts of frass. They feed on the outer layer of bark, not the interior xylem or phloem, so we don't see the upper dieback that we do with some other borers. Here is a fact sheet on the linden bark borer moth from University of Massachusetts Extension with some additional information:
https://ag.umass.edu/landscape/publications-resources/insect-mite-guide/chrysoclista-linneella-formerly-glyphipterix-linneella

I recommend you have a certified arborist do an on-site examination of the tree. Someone examining the tree in person will be able to see details that we can't from photos. Once they determine the cause of the frass and make a definitive diagnosis, they will be able to suggest the best management strategy.