Tabliss does not collect any data (of any kind), other than error reports.
Your settings are stored securely within your browser.
Your settings only leave your browser when Tabliss connects to external services to retrieve some information on your behalf. These services are only contacted if they are enabled in Tabliss. The services are:
DarkSky - Weather information for the "Weather" widget
GIPHY - GIFs for the "GIPHY" background
GitHub - Quotes for the "Literature Clock" widget
Google & Bing - Search suggestions for the "Search Box" widget (if search suggestions are enabled)
TheySaidSo - Quotes for the "Daily Quotes" widget
Unsplash - Images for the "Unsplash" background