I was on blood thinners for a year after heart surgery and had this problem the entire time. First the sensor. The bood would occasionally foul the transmitter to the point I had to change it out. The company, Dexcom, always replaced fouled sensors and the transmitter worked fine after cleaning with alcohol.
The pump catheter also bled, but it did not affect the performance of the continuous infusion. The company did say to be careful because if the catheter was putting insulin directly into the blood stream I could experience unusual lows. That never happened. Off the blood thinners and the bleeding is no longer a problem.