Not known for his hitting ability, Grzenda once grounded out to third base in RFK Stadium and received a standing ovation. On September 30, 1971, he became the last pitcher in the franchise's tenure at Washington, D.C., getting two outs in the top of the ninth inning before fans, knowing the team would be leaving for Dallas–Fort Worth after the season to become the Texas Rangers, stormed the RFK Stadium field, causing a forfeit. Thirty-four years later, when baseball returned to the nation's capital, Grzenda returned to the RFK field before the Washington Nationals' first home game, handing George W. Bush the ball he would use to throw out the first pitch.
As a fielder, Grzenda was charged with no errors during his eight-year career for a perfect 1.000 fielding percentage (6 putouts, 66 assists).[1] In 1969 he made an appearance in the ALCS for the Minnesota Twins.