It's only common sense to keep the kleenex box within client sight and reach, but as some others said, I would give the T a chance.

Ts that keep a box of kleenex in other places with the purpose of provoking actions in a client seem manipulative,

As someone with PTSD who is hypervigilant*, other signs of manipulation more impactful than a mere kleenex box would be on my radar. Avoiding manipulation and potential drama is not a bad thing. Not saying this T is like that but thinking of the themes in the thread where people stated therapists placed kleenex boxes purposefully to get clients to do things.

*hypyervigilance is not paranoia and has help kept me safe in avoiding problematic individuals. Learning how trauma survivors can become revictimized had led to more open mindedness about this.