I've never had any issues with Traveler Insured, it should be easy to get them to pay whatever they should. What are you trying to get that you aren't currently?
We were scheduled to return with TK from TLV on Oct 11.
We opened a claim for 'trip interruption' for the new tickets we purchased. The analyst came back saying this it not an 'interruption' but rather a 'delay' as the airline classified it as 'operational reasons'.
trip interruption = 150% of cost
trip delay = $200 a day
my return cost was $1500-1850 per pax
Traveler Insured said I need to provide proof this was trip interruption
this is the relevant policy doc