To remove products from a search without deleting the data forever is possible using the global edit function in IMerchant.   

Go to: Tools / Administration / Database Maintenance / Global Edits
From this menu, click on GLOBALLY EDIT PRODUCTS.

The Globally Edit Products looks similar to the regular product search.  Do a search for the items you would like to hide or remove from the main product search.   You will notice buttons near the FIND button on the top portion of the screen for GLOBAL EDIT, RETAIL GLOBAL EDIT and RESESERVE STOCK.  

Global edit will allow you to pick from selected items in your search or use the entire search results.  Highlight the rows you want to make inactive if not using the full search results and click GLOBAL EDIT button on the top with a green globe.

Click SELECTED OR ALL products to update in your bulk / global edit.

Next pick the column / data you would like to update.  If you want to hide products, you will be editing the ACTIVE column so click the checkbox next to ACTIVE.

Click NEXT - Enter new values for fields selected
In the drop down select NOT ACTIVE, this will change the products to not active and hide them in the regular search results.  You can always go back and find these later but regular search results will not show these.

Click NEXT - Update Records Selected
You will get a notice on the screen about updates done and click YES to refresh the screen and show your changes to the product search.

Once you click YES, the yellow lines you originally highlighted will turn GREEN and display the updated data.
(ACTIVE to NOT ACTIVE) - Click OK below to complete your changes.