Those instructions in full;
Turn off mains
Remove battery
Remove all traces of TP800 equipment
Place into bin
Contact a local installer, or, fit a DIY Scantronic 9651, Pyronix Enforcer, Accenta based kit, or, fit dummy box with a real brand on, ADT, Yale, Landsend Securities, John o' Groats Systems, it doesnt matter
You are now less likely to be burgled with none of the downsides of owning a TP800.
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Hi just for clarity a pir works using passive infra red to detect movement of heat, if the ambient temp is high then it will struggle to detect. A dual technology detector is two different types of detection in one Microwave which uses radar dopler to detect, and passive infra red, both radar doplar and the passive infra red have to detect before the detector activates. Which means you will still have the same problem with it not detecting.
Not familiar with the Pyronix tat so I could be wrong but surely all new kit is two way technology, therefore the detector wont be working while the alarm is unset anyway? HKC is the only manufacturer that makes a wireless DT not that it would work in your situ