EVERY FOUR WEEKS? Has your INR been that stable that the insurance company is comfortable with testing only once every four weeks? I'd be somewhat scared, too. (In my past, I've gone longer than four weeks on a consistent dose and pretty consistent diet, but it makes a whole lot more sense to be able to test more frequently).
The next time you talk to your insurance company, perhaps you can ask the bean counter at the company to compare the cost of more frequent tests (or a monitor and strips), to the cost of long term care if you have a stroke because THEY AREN'T AUTHORIZING TESTS FREQUENTLY ENOUGH. Remind them that your plan probably has a 2 or 4 million dollar cap - ant that, if you have a stroke because they decline to cover more frequent testing, you may just use all THEIR money up.
FWIW -- I've bought my meters on eBay - and, with two exceptions (both were advertised as As Is and untested or non-functional), they ALL worked just fine. I got strips either over eBay or had a doctor order them for me from a medical supply company.
The mantra on this forum has long been 'dose the diet,' not 'diet the dose.' It looks like this four week schedule has forced you try to 'diet the dose' - keeping you from making any changes because you don't have any feedback to tell you if you've done anything to change your INR. It's not fair to you. It's risky for the insurance company.
Back to the subject at hand, what you've said about Green Tea having Vitamin K and Black (or Orange) teas not having it, it seems that Black teas are safe.
Again - having a meter and strips, and being able to do self testing more frequently (or even within a couple days of falling off of a consistent diet or activity schedule) will help you be sure you're in range, and may even wind up saving you from a medical catastrophe (and your insurance from spending a WHOLE LOT OF MONEY). Good luck with your insurance company.