As a person who once thought that, once your INR was stable, and your diet and activities were consistent, frequent testing wasn't necessary, I now feel that weekly testing is SAFER than just testing monthly. An INR test -- any INR test -- is a snapshot of what your INR is at the time that you test. Doing a test monthly doesn't give you any idea what your INR was a week, or two weeks, or three weeks before the testing. If you start something like green tea - or anything else that may influence your INR - and don't do anything to detect whether or not there are changes in your INR - relying only on monthly testing -- you could be putting yourself at risk of something really bad.
Personally, I suggest that you get a meter -- there are some that are fairly affordable on eBay (and I have some that I may even be interested in parting with), and you can also get fresh strips on eBay and from other retailers. Ultimately, you are responsible for your own life, and I am no longer comfortable with believing that a once a month snapshot of my INR is really providing an adequate picture.
There was a time when the process of testing was kind of a bother -- you had to go to a lab, park your car (or take public transit to the lab), wait for a lab tech to take your blood, make the trek back home, and wait - perhaps a day or two - to get your results. It was probably fairly expensive. For many people, it was a pain that should be put off as much as possible. With the availability of meters for self-testing, this has gone away. An INR test could be as close as your kitchen, or living room, or bathroom, or wherever you are comfortable running the test. Once the meter is paid for, the test usually costs less than $6 or $7 unless you waste a strip, and you know right away what your approximate INR is. Other than financial concerns, and the fact that some people aren't candidates for self-testing, I see little reason why a person can't test weekly and have a better track of INR than a once monthly snapshot.
If you change meds (add an antibiotic or over the counter pill), or change diet, or do other things that you are concerned might raise or lower your INR, confirmation may be as close as your personal meter. I strongly suggest that you consider self-testing.