QB Issue Resolution:

Right Рyou can delete them after matching. In fact it will slow down processing if you keep a huge number of them.  When first running it there is a dialog that asks if you always want to delete them after matching. I always choose yes.

Resolution for Issue 'Is it safe to delete matched transactions from the “Downloaded Transactions” window that have been recorded?' available: Yes (Solved).
Source: Intuit Community forum.

Is it safe to delete matched transactions from the “Downloaded Transactions” window that have been recorded?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

Support for downloaded transactions
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