And how have the Mets done on days when Arsenal have won a trophy, you ask? Well, keep in mind, the Mets weren't founded until 1962, so the Arsenal trophies of 1930 to 1953 don't matter here.
April 28, 1970: Arsenal win the Inter-Cities Fairs Cup (the tournament now known as the Europa League), beating Anderlecht of Brussels, Belgium, 3-0 at Highbury. The Mets beat the San Francisco Giants, 5-2 at Candlestick Park in San Francisco.
May 3, 1971: Arsenal clinch the League, beating their North London arch-rivals, Tottenham Hotspur, 1-0 at Spurs' ground, White Hart Lane. The Mets beat the Chicago Cubs, 3-2 at Shea Stadium.
May 8, 1971: Arsenal win the FA Cup, clinching "The Double," beating Liverpool, 2-1 in extra time at Wembley. The Mets beat the St. Louis Cardinals, 9-5 at Shea.
May 12, 1979: Arsenal win the FA Cup, beating Manchester United, 3-2 at Wembley. The Mets lose to the San Diego Padres, 2-1 at San Diego Stadium, which would soon be renamed Jack Murphy Stadium, after the sports columnist whose advocacy got the city its major league teams, and was also the brother of longtime Mets broadcaster Bob Murphy.
April 5, 1987: Arsenal win the Football League Cup, beating Liverpool, 2-1 at Wembley. The Mets were scheduled to open their regular season 2 days later.
May 26, 1989: Arsenal clinch the League, beating Liverpool, 2-0 at Liverpool's ground, Anfield. The way the tiebreakers worked, Arsenal had to beat Liverpool by 2 goals, and get the 2nd from Michael Thomas in the last minute of the last game of the season. The Mets beat the Los Angeles Dodgers, 8-2 at Dodger Stadium in Los Angeles.
May 6, 1991: Arsenal clinch the League, beating Manchester United, 3-1 at Highbury. Actually, they clinched earlier in the day, without playing, when Liverpool lost to Nottingham Forest. The next season was the last for the old Football League Division One; thereafter, it would be the Premier League (again, herefore referred to as "the League"). The Mets are not scheduled to play on this day.
April 18, 1993: Arsenal win the League Cup, beating Sheffield Wednesday of Yorkshire, 2-1 at Wembley. The Mets lose to the Cincinnati Reds, 3-2 at Riverfront Stadium in Cincinnati.
May 20, 1993: After the Final ended 1-1 5 days earlier, Arsenal play Sheffield Wednesday again, in a replay, and again win 2-1 at Wembley. The Mets are not scheduled to play on this day.
May 4, 1994: Arsenal win the European Cup Winners' Cup, beating Parma of Italy, 1-0 at Parken Stadium in Copenhagen, Denmark. The Mets beat the Giants, 7-4 at Shea.
May 3, 1998: Arsenal clinch the League, beating Everton of Merseyside, 4-0 at Highbury. The Mets beat the Colorado Rockies, 5-2 at Shea.
May 16, 1998: Arsenal win the FA Cup, and the Double, beating North-East club Newcastle United, 2-0 at Wembley. The Mets beat the Giants, 4-1 at Candlestick.
May 4, 2002: Arsenal win the FA Cup, beating Chelsea, 2-0 at the Millennium Stadium in Cardiff, Wales. This was the seat of the Final between the 2000 closing of the old Wembley and the 2007 opening of the new one. The Mets lose to the Houston Astros, 3-1 at Shea.
May 8, 2002: Arsenal clinch the League, and the Double, beating Manchester United, 1-0 at United's ground, Old Trafford. The Mets lose to the Giants, 8-2 at Shea.
May 17, 2003: Arsenal win the FA Cup, beating Southampton of Hampshire, 1-0 at the Millennium Stadium. Again, the Mets play the Giants, and beat them, 5-1 at Candlestick
April 25, 2004: Arsenal clinch the League, with a draw against Spurs, 2-2 at White Hart Lane. Arsenal had now won the League at White Hart Lane as many times as Spurs had: 2. The Mets lose to the Cubs, 4-1 at Wrigley Field in Chicago.
May 21, 2005: Arsenal win the FA Cup, after drawing with Manchester United, 0-0, despite being down to 10 men, beating them 5-4 on penalty kicks, at the Millennium Stadium. The Mets must feel like they've won a trophy as they beat the Yankees in an Interleague game, 7-1 at Shea.
May 17, 2014: Arsenal win the FA Cup, beating Hull City of Yorkshire, 3-2 in extra time, at the new Wembley Stadium in West London. The Mets beat the Washington Nationals, 5-2 at Robert F. Kennedy Stadium in Washington.
May 30, 2015: Arsenal win the FA Cup, beating Aston Villa of Birmingham, 4-0 at Wembley. The Mets lose to the Miami Marlins, 9-5 at Citi Field.
May 27, 2017: Arsenal win the FA Cup, beating Chelsea, 2-1 at Wembley. The Mets lose to the Pittsburgh Pirates, 5-4 at PNC Park in Pittsburgh.
August 1, 2020: Arsenal win the FA Cup, beating Chelsea, 2-1 at Wembley. The Mets lose to the Atlanta Braves, 7-1 at Truist Park in Cumberland, Georgia.
Overall: The Yankees have won 10 games on days when The Arsenal have won trophies, lost 8, and were not scheduled to play on 3 such days.