I think this may sound strange and funny but this is what exactly happened: 

I was playing and at the same time, sending messages to my opponent.  (Greetings and making some friendly conversations) Suddenly, the page was like - being refreshed and there a certain note appears -You have a pending draw offer. Hmmp..  That was strange.

So I scrolled down the page lookng for an icon,  Refuse to a Draw - thinking I wasn't the one who offered it in the first place.  But there is none.  (or a refuse a draw or cancel a draw, or whatever)  Of course, I could simply tell my opponent that I accidently offered a draw and asked him politely to ignore it in which I already did.

However, can anybody please share an idea about this?

Under the provisions of article 10.7 of F.I.D.E. Laws of Chess ...

10.7

A proposal of a draw under the provisions of Article 10.6 may be made by a player only at the moment when he has just moved a piece. On then proposing a draw, he starts the clock of his opponent. The latter may accept the proposal, which is always to be taken as unconditional, or he may reject it either orally or by completing a move. A draw offer is valid until the opponent has accepted or rejected it. 
[The gamesmanship question "Are you playing for a win?" can be considered as an offer of a draw] .

... even if you make a draw offer accidentally, it is still binding.

Right!  No, I wasn't really winning.  I just want to continue the game to the end.

Thanks a lot, I don't know that.  Honestly, I really apreciate people who help in forums.  What you just told me was quite an enlightenment.

Anyways, looks like my new chessfriend ignored the draw as well, so we're playing it through.  Thanks again.

Yeah, it is not possible to take back a draw offer so be very careful when you choose to use the draw button!

And, interestingly, chess.com departs from the standard rules by allowing a draw to be offered at any time, even if  it is not your move. See discussion here.

That is interesting. What is the penalty for offering at the wrong time?

If you do offer at the wtong time, and your opponent accepts, can you back out because your offer was illegal? [edit: obviuosly I mean OTB, not here..}