The TERF goal is the same as the broader radfem goal of the 90s. It's to abolish the gender binary while having their cake and eating it too. Their goal as outlined in some academic feminist articles was to promote trends of non-binary, to undermine the acceptance of mtf as women, and stop losing ftm which they saw as women. TERFs don't make a sympathetic distinction at all.
Also how is transmedicalist offensive I thought they called themselves that?
Some might call themselves that because they're young or stupid and don't think it through. Transmedicalists is just a sanitized version of truscum, which is a slur. Therefore, transmedicalist is a derogatory label with the intention of othering and maginalizing trans people, by saying they're not the actual trans people, they're an extreme group. The discourse in NB and queer circles similarly revolves around projecting internal transphobia on that group of actual trans people, calling them bigots, and dehumanizing them with a poppy quirky and glittery vibe on sites like Twitter and Youtube. Inherently, because they want to push the idea that those trans people are brainwashed by the gender binary, and NB and queer are the true trans people that will smash the binary, like the genderfuck revolutionaries they are.
Transsexual/transgender was always a medical condition, not an identify or movement. They may have been involved with movements in the past, but the state of being trans was never political. The current "trans" community is a socio-political movement. "Transmedicalist" and other terms like "truscum" are modern inventions, aimed to rephrase trans stuff in relation to that socio-political movement, almost exclusively in a derogatory and dismissive way.
The same way trans people use "cis" and "afab/amab" despite that they originated outside of trans communities with othering intentions. When you use the slaver master's words to describe yourself, you're forever a slave in your own mind.