You may hire a professional installer to do so, or you could unclick the clock on the cork tiles carefully, replace the damaged tiles with new ones.

Best to hire a pro, rather than, trying to diy. You can jeopardize the orginal installation if, the repair is done wrong. It's not something you want to learn online. You need someone on-site to teach you. In order to get a good understanding on how-to.

fwiw, I had to patch a water-damaged interior section of my DR t&g oak floor. Right or wrong, I decided I could fit it best if I chiseled out the bad section and then used plain oak boards and a little glue to fit in the replacement pieces. My fix was more than 20 years ago and it still looks great. Maybe you could do something similar by removing the tongue on whatever pieces are required to fit.

eta: to be clear, I'd only resort to my approach if you are not able to unlock whatever you have in place.

The tiles aren't going to match until they've been in the sunlight for a year or so. Cork isn't ceramic tile.