[Obi_Juan_Kenobi]

The only 'signature' one could expect is from flanking sequences. Some viruses, transposons, and bacteria leave such sequence, but it is not universal. And we're talking about organisms here, whole genomes of many mega/giga-bases vs. viruses of mere kilobases. Even knowing what to look for, it can be quite difficult: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4940375/

In a lab setting, a simple restriction digest and recombination can yield a modification with no signature, or else you can generate SNPs with PCR. And you would want to, as viral genomes are so small, often with overlapping ORFs, that you don't have much room to leave a bunch of junk around.

There is no signature. What we can do is look at sequence similarity and decide how probable or improbable a given sequence combination is from the viral genome sampling available. It's a lot of handwavy Bayesian statistics, based on incomplete sampling.