I am not clear what your output is. If it was a PDF then you could add "Produced using a free trial by XXX, get your free trial here", or something along those lines. Then if they want that statement removed that is the upgrade. But this way it makes your product still look better in that the performance is timely etc.
Another option, limit the trial to 3, 5, 7 days, but let it be full extent.
If your output is csv or some raw data this adding a text message is pretty useless. Maybe you could instead limit the output to only the first page or first 3 pages, this way again it shows the full power and speed but limits the output to help entice an upgrade.
Just a few other points, with SaaS there are always people that will get what they need out of a free trial and never sign up, or they will intentionally sign up for a month and then cancel. I know I have done it and will do that in the future if I need to. So a certain amount of this type of churn is normal and expected. Maybe you also want to evaluate the numbers too. Lastly, if the people complaining aren't yet customers and are a small number of overall prospects then maybe this really isn't an issue and is just noise. Not all comments require a change.