Good Morning
I am sure it is safe to use the heating system, but as it gets used more, you may wake up to a cold house one morning.
From the sound of things, you used a heating company, not just a self employed contractor, so you should be able to call them back and require them to come and fix the problem. You should ask for a different service technician.It sounds like the guy you had was an installer and not a service tech. and does not do many cleanings, so he would be less trained. If your state has an oil burner license, does that person carry his own? or does he work under the company license?
I am not trying to put the guy down, just show that he may not have had enough cleaning experience and was hired by his company for installation purposes.
Also, if you have a service contract with that company that declined to refund your money, use the service, that is what it is there for. But they should fix this because it is there problem to start with.