Restart the device: Sometimes, the cache or settings of the device may cause some unexpected problems, such as the inability to delete bookmarks on the home screen. In this case, you can try to solve the problem by restarting the device. Press and hold the power button on the device, and then slide the slider or select the power off option. Wait a few seconds, then press the power button to restart.
Clear Safari Cache: If the bookmark you want to delete is a bookmark in Safari, you can try clearing Safari Cache. Open the Settings application, select Safari, then slide to the bottom of the page and select "Clear History and Website Data". This will delete Safari's cache and history, and all Cookie and cached data. Please note that this will delete all the website data and login information, and you need to re-enter these information.
Use Safari when deleting bookmarks: long press the bookmark you want to delete and select the "Open in Safari" option. This will open Safari and load the website. In Safari, click the "AA" icon next to the address bar, and then select Website Settings. On the "Website Settings" page, you can find the "Save to Home Screen" option, click this option, and then select "Delete Offline Data". This will delete the bookmark of this website on the home screen.
Delete bookmarks through iTunes: If your device is connected to your computer and syncs with iTunes, you can delete bookmarks on the main screen of iTunes. Open iTunes, and then connect the device to your computer. Select the device icon, and then select the Information tab. In the Advanced option, you can find the Home Screen Layout option. In this option, you can delete bookmarks on the home screen. After deletion, select the Apply tab and click the Synchronize button to synchronize the device changes.