Foreign, in this case, means outside of the species and even outside of the animal kingdom. The article suggests that the tardigrade DNA includes genes from “plants, fungi and Archaea, [aquired] through a process called horizontal gene transfer…”

“We think of the tree of life, with genetic material passing vertically from mom and dad,” said Boothby. “But with horizontal gene transfer
becoming more widely accepted and more well known, at least in certain
organisms, it is beginning to change the way we think about evolution
and inheritance of genetic material and the stability of genomes. So
instead of thinking of the tree of life, we can think about the web of
life and genetic material crossing from branch to branch. So it’s
exciting. We are beginning to adjust our understanding of how evolution
works.”

so there is a suggestion of a web/network/graph of lifee with a rhozomatic gene transfer?