More on my tubular adventure... I think two of the tires I wound up with were new, some Continental Competitions.
They have tubular tape on them but it was only partially covered and who knows how long it had been there. As I don't use tape, I decided to remove it. I wasn't sure how to go about that, but decided to try some rubbing alcohol and scraping with the blade of a utility knife. It's slow going, but seems to be working, and the rubbing alcohol doesn't seem to be affecting the adherence of the base tape. (While the tape looks like reinforced packing tape, the reinforcing strands aren't anywhere nearly as strong as the real thing. The adhesive is much stronger than the "reinforcing" strands, even after application of rubbing alcohol. It's slow going, but I'm retired, so I sometimes get to do what I want.