How is rheumatic fever and a heart murmur linked?

Valve damage. Rheumatic fever may damage or distort the valves in your heart rendering them unable to either close or open properly. As blood is pushed through a valve that does not open properly or leaks back through one that does not close well, the "squirting" noise (murmur) that is produced with acceleration of blood flow can be heard with a stethoscope placed over the affected valve.
Heart valve damage. Rheumatic fever causes damage to heart valves which gets worse over time. The damaged heart valve causes the murmur.