First of all and above all
we cannot give medical advice which is contrary to what is recommended by your doctor. If you have any concerns about your medication, please seek the advice of your doctor before making any changes to dosage or other recommendations
What research states
Research has shown that certain fruits, particularly grapefruit and other citrus juices, can interfere with medication efficacy. A review in the journal Pharmacy Practice sought to explore warfarin interactions involving fruits to see which fruits were most commonly associated with these interactions. Twenty-three case reports and controlled clinical trials were evaluated and the majority involved cranberry products (also the most frequently studied fruit). Pomegranate juice, avocado, grapefruit juice, mango, and papain were also suspected in the reported warfarin–fruit interactions. Based on these limited findings, additional research is needed but physicians may want advise patients taking warfarin to consume cranberry products and grapefruit juice in limited amounts and to inquire regarding recent mango, pomegranate juice, and avocado consumption. (Source: MPR)
You can read the full article referenced in MPR at this web address
Adepoju & Adeyemi (2010) also states that it has been found that Limes and Lime Juice (which are citrus) cause a reduction in the anticoagulant activity of warfarin.
From what I have found, it is not just the citus content which needs bearing in mind. As @DoctorWhom stated in the comments, "Warfarin needs to be monitored regularly by your doctor's office. As it's a Vitamin K antagonist, eating foods high in Vitamin K reduces its effect".
Livestrong states that
Phylloquinone, or vitamin K1, is the major form of vitamin K in the diet. According to the Cleveland Clinic, foods very high in vitamin K include broccoli, cauliflower, cabbage, soy oil, green tea, tofu, spinach and other dark leafy greens. For those who take warfarin, it is recommended to avoid large fluctuations in vitamin K intake. Large amounts of vitamin K can cause the drug to become less effective, and consuming vitamin K in smaller amounts than is customary for a particular person may increase the effectiveness of the drug and result in bleeding. Maintaining a consistent intake of vitamin K in the diet will allow the physician to make the most therapeutic changes to the warfarin dose.
Whilst it is possible that citrus foods can be eaten, it is advisable to consult your doctor before doing so to ensure that the correct information is given for your personal situation
Whatever you do, do not go against advice given by your doctor as it can risk your life when on blood thinning medications such as Warfarin or any other (complimentary or alternative) blood thinning products