HGTV Couple Demand Accountability From Pro Pet-Sitter and Rover.com

1 PM PT -- The former professional dog-sitter who lost her job at Rover.com has now been kicked off her jiu-jitsu club.

Miami's Fight Sports Club tells TMZ they just learned of the incident, and said both the pet-sitter and her boyfriend have been banned from the team.

The academy said ... "We are very sad and deeply sorry for this situation. ... We want to make it clear that we have no involvement or responsibility for anyone’s personal life or business outside the academy. Fight Sports stands for truth, values, and integrity, and we will always take action when something goes against those principles."

The HGTV couple who say their dog was killed while supposedly in the care of a professional pet-sitter is demanding accountability ... and, they're thinking about ways they can redefine the legal status of dogs in Florida.

We spoke with Eilyn and Ray Jimenez -- best known for starring in the hit reality show "Divided by Design" -- on "TMZ Live" Friday ... and, they ran through the events surrounding their dog's death, which they previously laid out on social media.

ICYMI ... Eilyn and Ray were told their dog Aria -- a 12-year-old Shih Tzu -- died of a heart attack while in the care of a pet-sitter while they were out of town for 2 days. However, they said they learned from the cremation center where their dog was taken before they got home that their pup was actually killed by another dog.

Adding insult to injury, they say the pet-sitter wasn't actually around to look after the dog ... she had flown from Florida to Las Vegas for a jiu-jitsu tournament -- and actually posted on social media about it -- while she was supposed to be watching the dog. Her boyfriend was actually taking care of Aria ... which is how the poor pooch ended up dead.

The Miami couple says they're shocked at the pet-sitter's bald-faced lies to them -- they say she even burst into tears while telling the couple the elaborate fabrication -- and, they want accountability.

They tell us they've been in contact with Rover.com ... they say the company told them this poor excuse for a pet-sitter has been fired. The company also offered them $1,000 for their dog's death.

Worth noting ... in a statement to us, Rover said, "Upon learning of this incident, Rover’s 24/7 Trust & Safety team conducted a thorough investigation into Aria’s passing. The sitter involved has been deactivated from our platform without the option to appeal .... We stand ready to assist law enforcement with their investigation should they become involved."

As for whether they might take Rover.com to court to get the accountability they're seeking ... the couple says their main focus is to change the legal status of dogs in Florida -- arguing they're family, not property, as the law currently holds.