Nearly 9 years ago, I did extensive “newsgroup” research on ventless gas logs in preparation of launching the very first fireplace web site on the Internet…which specializes in gas logs.
I read posting after posting just like yours about ventless gas logs emitting odors. The smell has commonly been equated to the smell of burning kerosene.
People with sensitive noses complain about the smell...others say it doesn't bother them and kind of reminds them of "Grandma's House".
I read about excess moisture in the air that produces mildew...and ice that melts in chimneys leaving pools of water in living rooms (because the by-product of burning natural gas is H20…which can freeze in the chimney…and then thaw out).
In the infant years of our web site, we avoided selling ventless products of any type for fear of customer dissatisfaction, or other liability issues.
However, as the years passed and the popularity of ventless products grew, too many of our visitors began requesting them and we eventually had to start selling them to remain competitive.
We are very careful to inform every customer who seeks to purchases a ventless product that the odor is just but one of the negative features. We do not recommend them...but people buy them from us anyway.
What you are experiencing may just be the normal mode of operation for the product you purchased. However, the smell could also indicate that it is not operating properly and could present a health hazard.
You may do well to have your local gas company (or whatever other resource you have) check to see if the logs are producing unsafe levels of Carbon Monoxide or if they are depleting too much oxygen from your home.
If they check out to be operating safely, you may not be able to do anything about the smell and may simply need to burn them with the damper fully open and a window cracked.
Anonyms Gas Log Expert
P.S. In California ventless products are illegal due to strict rules about indoor air quality.