Should motor oil grade matter?

No it’s close enough. It’s slightly thinner oil so it might get into the engine and lead to smokey engine if the car gas a very high mileage but doubtful.

The 5 part is more important because it effectively controls the lubrication at low temperature and start up when most wear occurs.

Yes Tommy, it does. And PLEASE don't mix one grade with another. 5w gives you a wide range. Wider than 10w. If you don't have an owner's manual, google it. There will be an Oil Maintenance Chart. It will show various grades & climate temperatures.

For your purposes it is not going to matter. But I would think it would be easier to get 5W30 over 5W20.  If you can remember the brand or color of the bottle, get the same stuff as the detergents in the oil remain the same.

Absolutely! The GM Engineers recommend 5W-30 for your motor as listed in the glove compartment manual. The machined clearances throughout your engines are provided in a new engine so that the oil should act as a 5 weight when it's cold and a 30 weight when the motor is up to maximum operating temperature. Now consider this: When mileage is added machined clearances increase so you do not want an oil that's a lower viscosity (thinner) at full operating temperature. Sorry I miss-understood your question. One quart of 5W-20 to top-off between regular oil changes wouldn't hurt anything *But, if your engine uses more than one quart between regular oil changes I would stick with 5W-30.

All cars can take a large range of different viscosity oils. So 5w-20 will be fine for topping up purposes.

Really when mixing one quart of oil that is slightly thinner at operating temperature with four quarts of one grade thicker will produce an almost indistinguishable difference. 

Actually when oil gets dirty it gets a little thicker, a quart of thinner oil might return it to original thickness.

It's better to add 5w 20w then to be low on oil but use the correct weight oil when you change it. 

It is certainly better than driving with low oil. Engines with variable valve timing use oil pressure to phase the camshafts and require very specific viscosity to function as intended by the engineers. Using other than the recommended viscosity can hurt performance.

If you look in the owner's manual , it will probably give you a chart will the acceptable viscosity of oil. This is a measure of how thick it is, not the grade. This 5w20 will give you an average viscosity of 5w27 1/2.

 I will bet that 5w20 will be fine, except in extremely hot climates.  When you get your oil changed, get the proper stuff.

The manufacturer was kind enough to put the grade on the oil cap so you do not have to look at the manual and you did not follow it.  You need to get your head examined.