Yes, the GL and asset system must indeed match. So, hopefully you have a system where you can remove the item in the asset system and this will automatically create the required entry to remove it in GL. If not, then keep in mind you WILL NEED to make an entry in GL. Example you want to remove a fully depreciated asset that has a cost of $1,000. In the GL right now the asset is in fixed assets with a $1,000 debit balance AND in the Accumulated Depreciation account the asset has a related $1,000 CREDIT balance. So you do need an entry to remove those two amounts.
As you do this removal of assets be advised of the following:
Some states, like Calif, assess business personal property tax on assets that are still in use - whether or not you wrote them off. So if you use the fixed assets listing to prepare your personal property tax report you will need to add back in the assets that are still in use but no longer on your fixed assets because you wrote them off.
Same issue happens for income tax depreciation, so speak to your tax preparer folks before you do the write off so that everyone is on the same page.