A person gave something to a friend, so his friend said to him ‘jazak-Allahu khayran." He replied "That's ok" Is there any violation of islamic Law here? Has any disbelief occurred? He says he just meant that he does not demand any thanks or praise for his actions.
When someone, in response to some good turn on your part, says to you: "May Allaah reward you with good." (Jazaak-Allaahu khayran), the appropriate thing to say is something like: "And you as well" (wa iyyaaka) or "And may He reward you." (wa jazaaka). At the very least, he should say amin in response to the supplication that is being made to Allah on his behalf.
A reply of "that's alright" or "that's okay" is not appropriate. However, there is no sin or serious objection for doings so. As for the misgivings that you are having that your reply implicates a rejection of Allah's blessings, these are the mere whisperings of Shaytan. A person who suffers from such baseless misgivings should blow to the left three times and seek refuge with Allah from Shaytan three times He should also take care to recite the supplications of the morning and the evening and to keep his tongue moist with the remembrance of Allaah.
Otherwise, he subjects himself to the danger of being susceptible to Satan's whisperings, similar to the misgivings that you describe in your question.
And Allah knows best.