Harrison shrugged off Garcia's tweet: "Lol we talking real fighting now not some staged fight.
"How about beat someone that isn't picked from the old folks home and has a real heartbeat and then you can put my name in your mouth.
"Until then watch me win another mil."
Garcia responded: "I made more money than you winning without a sweat but now you are disrespecting the other girls I fought!
"Do you want to put your single million and I will put a million also to make this fight? Or will you make an excuse.
"U are a joke!"
Fellow MMA star Liv Parker chimed in, backing Harrison.
"She (Harrison) would probably be more interested in a quality opponent," Parker tweeted.
"If you want to talk jokes, you (Garcia) are the one fighting 50+ year old has-been wrestlers who are 1/4th your size and weight."
When flyweight Tara LaRosa defended Garcia, Parker added: "Do you really think she (Garcia) can be taken seriously given her track record?
"I also know how hard the women before me, yourself included, have fought to pave the way for women in the sport & her antics just feed the critics even more. Not who I want repping me as a female fighter.
"Just my opinion though … just hard to respect how she has carried herself."
Harrison is a two-time Olympic gold medallist in Judo and is considered one of the greatest female fighters of all time.
The American, who used to train with former UFC champ Ronda Rousey, is unbeaten at 8-0 since her MMA debut in 2018.