While a quart every 4 K miles is annoying, I do not think that would be enough consumption to get anything fixed if it were still under warranty.
That generation of 2.4 has the Earth Dreams i-VTEC technology engine with the variable intake valves system. It is very important to keep the small passageways and screen for the oil for that system clean, because it uses the engine oil like hydraulic fluid to move the variable valve system, and to kick in the second intake valve when the RPMs get high enough. That system is one of the reasons they get good MPGs for there size.
I have the same engine in my 2016 CR-V EX, though with only 26,XXX miles on it, mine does not consume much oil.
If it were mine, I would just top it off every couple of thousand miles, and stay with a good 0W-20 known for high cleaning ability such as Pennzoil Platinum, or even better yet if you can find it Pennzoil Ultra Platinum.
If it has over 75,000 miles you might run the high millage versions of those oils.
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Also don't forget to change the CVT fluid on it often, and ONLY USE HONDA HCF-2 FLUID IN IT. Honda CVTs are known to not work well with off brand CVT fluid. Changing the CVT fluid is super simple on a Honda CR-V. There are YouTube videos on how to do it. Be sure to use a torque wrench to tighten the drain and over-flow bolts. You will need a 3/8 inch drive torque wrench. Teckton torque wrench are very good quality at a lower price than some others good ones such as Snap-On. The drain gets tightened to 36 Lb ft. and the over-flow gets tightened to 15 Lb ft. Be suer to always store torque wrenches set to 0 or the lowest setting so the spring in them is not compressed, which could affect the calibration if left at a high setting for a long time. The over-flow is a 12 mm and is a little hard to find. They both have crush washers. You can reuse the old crush washer a couple of times. Do not loosen the one bolt that is also in that area that does not have a crush washer on it. A breaker bar or a pipe extension on your ratchet makes loosing the drain and over-flow much easier. Never use a torque wrench to loosen a bolt or nut. You might apply too much force to it and affect the calibration.
Do not wait for any maintance reminder of the vehicle to tell you to change the CVT fluid. You should change it every 30 K miles, or every 25 K miles if severe service. Severe for a CVT includes hills, and or a lot of stop and go driving, and or a lot of variation of speed, and or loading the vehicle up with a lot of weight often, and or towing. Easy service on a CVT is driving it long distances with little variation in speed. OEMPartSource.com sells original Honda parts and fluids for much less than any dealer.
Some even change the CVT fluid more often than that. You only get 1/2 the old fluid out with a drain and fill. So driving it some to mix the new with old and doing additional changes does remove more particulates and old fluid. I did my first drain and fill of the CVT at 25,0XX and second at 26,0XX miles and will be doing a third at 27,0XX. I plan to keep my CR-V a long time. And after those drain and fills probably will be doing a drain and fill about every 10 K to 15 K miles. For what a dealer charges for one CVT fluid change, I can buy the fluid and crush washers from OEM and do it myself 3 times. And with a dealer doing only 1 you are left with 1/2 the old fluid in it. By doing 3 myself I will be left with 12.5 % old fluid in it, for the same cost. That is much better than still having 1/2 the old in it. CVT transmissions use the fluid for multiple purposes, including making the parts move with hydraulic pressure. If the fluid has too much particulate in it those hydraulic systems can not function properly and that can cause the transmission to be damaged. So because I plan to keep mine for a long time, I change it often.
There is a CVT filter located on the upper right front of the engine compartment. But that should be good for something like 80 K miles before requiring change. There is also a YouTube video on how to do that.