It's just a question of chess etiquette: practically speaking, you get one draw offer per game, unless your opponent subsequently offers you a draw and you decline and continue play (and how often does that happen...?). Anything more is rude at best and harassment at worst.
Since this is the internet, rude behavior is, alas, to be expected frequently. So when it happens, just decline obnoxious draw offers and make sure you try extra hard to nail them.
One thing that might solve the problem (assuming it really is a problem...) would be to borrow an aspect of the doubling cube from backgammon. In backgammon once you double, your opponent gets control of the cube if he accepts the double and you can't double again.
The chess variant would work similarly to normal chess etiquette: either player can make the first draw offer, but if your opponent offers a draw and you decline, you get control of the "draw cube" (or token or whatever...) and now only you can offer a draw (or vice versa). Of course, there are enough things that need doing/fixing around here, I wouldn't even bother asking for it as a new feature.
Just play your move and ignore it, tbh i can think of a million things more distracting then a draw offer message appearing in chat