Ok, I need to determine if its a combustion noise or a blower noise, when the furnace is off and then it starts the burners which will light about a minute before the blower starts do you hear the noise then or does it come when the blower starts, if you don;t know please run a cycle like that and try to note that info.
It sounds like it is , and its not uncommon for the pulse furnace, you will need to have a service out to replace the flapper and check the heat exchanger , its probably just the flapper and a tune-up. Not really a DIY project , I don't think there is any danger in running it but always have a CO detector just in case.
Its part of the burner air intake like a diaphragm , being 20 years I guess I didn't think about the warranty or recall, was just answering the noise question. Usually its the source of a noise when it is failing but I also said to have it tuned up and heat exchanger checked, they should be able to do this in one call in less than an hour.
The part cost is very low on this, I would figure this whole service being done on regular time rates should be less that 250 dollars, in my opinion it is money wasted though unless you can get another year out of it besides this year.
More than likely it will last especially if it has just started, I can not guarantee it will not leave you without heat and in need of emergency service one day but if the noise is going away after start up its probably going to last for a while yet. If it's me , I run it and replace it in spring or before next heating season.