Did you set up Sync and this is not what you use on your Mac? Unfortunately, search settings are not currently included in Sync, so the search engine preferences need to be adjusted manually.

For steps to change your search settings, see these articles:

• Change your default search engine in Firefox for iOS
• Enable or disable search engines on Firefox for iOS

Sorry, you mentioned laptop as well as iOS. If you meant MacOS, try these articles instead:

• Manage Firefox search settings
• Add or remove a search engine in Firefox

And if on your Mac your home page or search setting keeps getting hijacked, check for unwanted or unknown extensions on the Add-ons page. Either:

• Command+Shift+a (Windows: Ctrl+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then cast a critical eye over the list on the right side. All extensions are optional. If in doubt, disable. If you find anything called Searchme you could just remove that.

Often a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Any improvement?