The lawsuit, filed in the US on Thursday, claims that Isaac Kenevan, 13, Archie Battersbee, 12, Julian "Jools" Sweeney, 14, and Maia Walsh, 13, died while attempting the so-called "blackout challenge".
The complaint was filed in the Superior Court of the State of Delaware by the US-based Social Media Victims Law Center on behalf of Archie's mother Hollie Dance, Isaac's mum Lisa Kenevan, Jools' mother Ellen Roome and Maia's dad Liam Walsh.
In the interview, Ms Kenevan accused TikTok of breaching "their own rules". In the lawsuit, the families claim that the platform breached the rules in a number of ways, including around not showing or promoting dangerous content that could cause significant physical harm.
Ms Dance said that the bereaved families were brushed off with "the same corporate statement" showing "no compassion at all - there's no meaning behind that statement for them".