Sources connected to the TLC reality show tell us … “Ink” execs felt they would be “sacrificing the integrity of the show” by ignoring Kat’s headline-making relationship and break-up from James in tonight’s season finale.

As we previously reported, Kat flipped out a few weeks ago when she saw a preview of the finale — which featured the relationship — and demanded producers either pull the footage, or she would refuse to participate in future production.

Kat lost that battle — but she did score ONE victory … we’re told producers did agree to cut some controversial footage showing Kat bad-mouthing another one of her exes, Nikki Sixx.