The union partly blames Ms Feltz for threats to the future of the BBC's Pebble Mill studio in Birmingham because she refused to have her new daytime show recorded there.
Ms Feltz's sense of her own talent and worth seem to have made her a lot of enemies. Many of those who have worked for Britain's own Oprah Winfrey have found her demanding and ambitious.
Before annoying Bectu, she annoyed the team that makes the Kilroy confessional show, broadcast immediately before her programme. Feltz demanded that it drop its trailer asking for people to phone if they want to be on the show because it was giving viewers time to switch over before she came on screen.
And previous to that confrontation the entire ITV network fell out with her. Feltz parted company with Anglia last year when she demanded a massive increase in her salary and more evening peak-time programmes.
ITV called her bluff, but the BBC, reviewing Feltz's ratings performance, paid her pounds 2m to come aboard to try to threaten ITV's dominance of the morning schedules.
But the BBC and Feltz have both been disappointed. Her replacement on ITV, Trisha Goddard, has been getting double the 700,000 viewers The Vanessa Show has pulled in at the BBC - hence the desperation to blame Kilroy.
It is an unlikely career for a girl who attended Haberdashers' Aske's girls school in London and read English at Trinity College, Cambridge.
After university, she entered journalism, working for the Jewish Chronicle and the Daily Mirror.
Although she often refers to her sheltered upbringing and conventional, stable marriage, she initially specialised in outspoken sex advice, even writing for the top shelf magazine Men Only.
She then worked for the BBC's London radio station GLR. Her break with Anglia's Vanessa show came in 1994.
When Paula Yates left Channel 4's The Big Breakfast, Feltz inherited the show's bed interview. She then gained her own consumer programme offshoot, Value For Money.
Feltz is reported to have turned down a multi-million pound opportunity to host her own chat show in the United States, as she prefers to stay with her family in Britain.
Proud of her family, she rarely gets through a news-paper or magazine interview without mentioning her surgeon husband, Michael Kurer, or her two children, Allegra and Saskia.