I would strongly suggest to do the injection in a saline solution, or a buffer solution (taking in consideration the concentration of glucose in it, to make the correction if necessary). The osmolarity of the internal medium would be altered if using water.
H2O or whatever makes you feel better - result will be the same!
The only thing that may be slightly useful is to bring the pH to 7.0 - 7.4.
Normally one uses saline or buffered saline for injectable test compounds (particularly IV) to keep the solution isotonic (equivalent to 0.15M NaCl) to prevent osmotic shock. In case of concentrated glucose, the solution is already very hypertonic and one can obviously not make it isotonic by adding NaCl or PBS to it (20% solution in your case is already 1.11M which is equivalent to 0.555M NaCl, as far as osmolarity goes).
The volume contribution of injected glucose to blood, in case of IV is minimal, therefore no major change is expected. Water has no pH buffering capacity that may be of concern.
The cited publication uses 5 successive injections of only water at 10% body weight over a period of 5 days. It is safe to say that this publication has absolutely no relevance to your question.
I am strongly against you using pure water, i would suggest if you can not get phosphate buffer solution, you used normal saline. oral glucose test have also shown to be the best.
I am not asking about why glucose tolerance is conducted. I have specific question and link you have provided does not answer! Do you have good points why saline not pure water should be used to make 20% glucose solution for i.p. injection in mice?
I believe your only concern would be molarity and sterility of your solution. You can't handle molarity if your glucose solution is 20%. For sterility, use only commercially available injectable water or normal saline. Both will not effect molarity. However to manage such high molarity, make sure that you inject this injection very very slowly.