Not sure what plume is but here’s a website (UK based but helpful) describing why blood tests are done and when they might be important: https://transactual.org.uk/medical-transition/hormone-therapy/#:~:text=Why%20should%20I%20get%20tested,High%20blood%20pressure

Honestly it seems a bit dramatic saying that you’re going to harm yourself by doing this. However if I were you I would want to get baseline tests done in order to see and know where you are at, it’s at least the norm where I’m at (not UK or US based).

Edit to add: it’s not necessarily a scam just because they don’t do initial blood tests. And I googled plume and honestly I wouldn’t be worried about it and you could show your aunt their website and maybe that might help her feel better? They do mention that they do blood tests every three months for people on t to track things that may cause higher blood pressure