can scientists see if a person's DNA has been genetically modified?
Nobody's DNA has been modified so far, so this question can only be answered in theory, not in practice.
In theory, about the only way I can think of that a genetic condition could be identified as "artificial" would be to compare the DNA to the parents and see if there was a change which did not arise from either parent or was too extreme to have come from a mutation. That might not be an absolute test, but it could be a high probability indicator.
Other than that, there is no specific difference between a naturally occurring gene and an artificial one.
The only other situation I can think of would be if certain genetic sequences become patentable, in which case they could be identified. I think there are real world patent cases already pending in anticipation of CRISPR designed gene and DNA sequences.