No, you should not delete a rental property asset just because it has been fully depreciated. As long as it is still in service, the asset remains an important part of your rental property's financial records.
If you sell (or dispose) of any rental property asset, then you would need to report that sale (or disposal) on your tax return. If an item is fully depreciated, then all the proceeds from the sale will be taxable. You would report the sale of an individual asset in You can report the sale in the Assets / Depreciation interview of the Business Income and Expenses > Rental Properties and Royalties section.
If you sell the entire rental property, you will report the sale in the same interview. For additional guidance, see: I sold my rental property. How do I report that? If selling the entire property, along with its associated assets (e.g. appliances, floor coverings, improvements, etc.) you will have to allocate the total sales price to the assets you are selling. The following post discusses this process: Sold my rental property
