First of all, be extremely careful with this material -- it causes severe damage to the lungs and eyes.  Use it only in the hood, and wear gloves and goggles.

There should be no water in it, as it is reactive with water, releasing methanol.  Simple distillation should drive off any methanol present, while any hydrolyzed materials will remain in the pot.

The rate of hydrolysis at pH 6 and room temperature  is not that fast. From this study (Chem. Mater. 1990, 2, 372-376; Effect of Solvents on the Hydrolysis Reaction of Tetramethyl Orthosilicate) I estimate the half life of TMOS a few hours in water at 25°C (it may be much longer for a trace of H2O in TMOS). Depending on the requirements for dryness, you may try phosphorus oxide (very efficient but agressive; may react with the silicate), molecular sieves (pellets: no filtration needed, calcium chloride, magnesium sulfate (less efficient but not reactive) ... etc.   

Perhaps a distillation in the presence of some calcium hydride?

Good idea! CaH2 is basic and reductive instead of acidic as most drying agents. Caution: hydrogen gas is generated in quantity depending on the amount of water.

Please check:

PURIFICATION OF LABORATORY CHEMICALS.

Fourth Edition

Armarego and Perrin. 

Page:

438