Reimer participated in his first Paralympics Game in 1968 in Tel Aviv. Competing in table tennis, swimming, and track events, he won gold at the Men's Discus Throw B with a distance of 27.47 metres. He also placed first at the Men's Club Throw B with a throw of 42.01 metres, beating the silver medalist by nearly 16 metres. At the Men's Javelin Throw B, he placed second with a throw of 36.21 metres.