Solution for Microsoft Teams is available since Quick Links Web Part version 22.214.171.124.
- Open the Team on Teams panel that you intend to add the Web Part;
- Click on the [+] button to add a new Tab to the Team;
- On the Search type Quick Links and select the BindTuning Quick Links
- It'll open a modal where you can post that you've added a new tab or not. After selecting either or not to post, click on Save.
- The tab will be added to the team.
Now the only thing left to do is to setup the rest of the Web Part Properties.