It might be useful to examine what makes them take offense. A lot of words can cause offense, such as bigot (which is appropriate in many cases here), but is still not a slur (and still often true).
In the case of TERF, it stands for Transgender-Exclusionary Radical Feminist. it was coined by a cisgender woman who was tired of radical feminists being saddled with the transphobic mantle when only a handful of them were transphobic.
Near as I can tell, when used appropriately (which is a totally different conversation) the term is simply calling out those who identify with so-called feminist beliefs that discriminate against or otherwise hurt trans people. Since, when used appropriately, the term refers specifically to feminists who discriminate against and lead a hate campaign against transgender people, TERF's have no legitimate claim to offense if the label is applied correctly.
It's true the term is over used and often misapplied. Grahm Linehan is a transphobe but probably not a radical feminist. So too a lot of garden variety anti-trans bigots who have been called TERFs. However, I don't think that's why the term has caused offense. Very seldom would I expect someone to say they were offended by being called a feminist and get any traction from it.
Therefore, I really don't understand this claim to offense, other than it makes them look bad (and if they know enough that being called anti-trans is bad, then they maybe shouldn't express anti-trans views).
Maybe you have a better handle on why someone who is transphobic would legitimately be upset for being called such? I would be interested in hearing it.