Yes, in most cases you can control what appears on your portal rather than showing every single option your suppliers return. Most travel businesses want this at some point, either because they have a direct contract with certain hotels they would rather sell, or because there are airlines or properties they have had problems with and do not want to offer to their customers.
The usual way this works is through settings on your portal that tell it what to include or leave out of search results. Depending on what you are selling, that can mean switching a whole supplier on or off, limiting results to certain destinations or regions, hiding specific properties, or excluding certain airlines or fare types. Once the rule is saved, your customers simply never see the excluded option, so there is nothing for your staff to remember or filter by hand.
How far you can go does depend on your plan and on the agreements behind each supplier. Some suppliers send their content as a single feed with limited room to pick and choose item by item, and some contracts expect you to display what is offered. It is also worth being careful about blocking too much, because in smaller towns or on quiet dates you may be left with thin results and lose bookings you would otherwise have taken.
The sensible next step is to write down exactly what you want to exclude and why, then go through that list with your account contact so you can see which parts can be set up as portal rules and which depend on the supplier.