How can I remove CWM from my Xperia Neo V?
EDIT: I have obviously rooted my device but I did not unlock the bootloader. (At least I assume that I didn't do it accidentaly -- in any case, I didn't root my phone using the official method.)
The boot loader is unlocked yes? If it is, I am not certain if it can be re-locked again for the OTA update to proceed.
Do not accept OTA updates if the bootloader is unlocked!
Best bet would be to use the Sony's companion phone software under Windows and let that update it manually instead :)
Do not try that in a virtual machine/virtual box/vmware!
Why don't you go into Settings > Applications > Manage Applications, then uninstall it from there, or if you have Titanium Backup installed, just un-install it from there. Its an ordinary apk app, that is somewhat, IMHO, misleading. I'll explain why in a minute.
Sony has this strange and unusual concept of recovery/bootloader. In general speaking, there is two partitions out of many, for the sake of the edit, I am specifically focusing on boot and recovery.
The general consensus is this, there's two partitions, boot and recovery, boot is what you know, is responsible for bringing up the system when the power key is pressed. This is highly specialized machine code that is tied intimately, as per the manufacturer/OEM.
Recovery on the other hand, is where you can do basic recovery, that is, clean the data and cache partition, and re-flash the stock ROM as indicated by the OEM.
In Sony's case, the reason, that your so-called CWM is in fact an APK is because, it would p^&$ off a lot of users if it was installed directly on the recovery partition, ... the big gotcha... yes, there is, for some obscure reason, Sony decided to bundle Boot and Recovery into the one partition, that's where the danger lies with Sony handsets, flash it directly into that, its buh-bye to your handset.
As for accepting OTA updates if bootloader is unlocked, there's some mechanism or checking going on in respect to the OTA zip file (I'd guess) for the presence of locked bootloader hence the warning I mentioned above. Use the Sony PC Companion suite software for Windows if you express a desire to go with the official updates from Sony.
So there you have it, a bit of knowledge and empowerment in understanding the nuances of Android when it comes to manufacturers. Yeah, I don't understand myself why the two are "merged" into one partition as a result, hence there will be the danger of messing up Xperia handsets.
What got me questioning about it was, why the .... was it being dumped into /system directory which is where the real ROM lies in, then it dawned on me the reason, that's why there's a big fat warning and notice about unlocking bootloaders via the Sony way.
IMHO, there really should be two partitions - boot and recovery, after all, if that's the case, it would make modding and customizing even easier but maybe due to whatever reasons Sony had, they decided to have that combined into one.
(Samsung has definitely the two partitions but its not as easy as it sounds but that's a discussion for another time :) HTC is the same as Samsung, Zte - which I have the Blade in my possession has the two hence its popular on modaco due to the ease of hacking and modd-ability)
In fact, you can actually still flash custom roms even with the bootloader locked - that was news to me but I'll leave this edited answer for now.
I think there's a reason you're having a hard time finding information about how to relock the bootloader and install the OTA: according to this thread you might brick your phone with the OTA update. Why do you want the OTA instead of some custom ROM to begin with? Are there any unique features? I'd play it safe if I were you and just go with custom ROMs in the future as well, mixing it up doesn't seem to be a good idea.
edit I'd like to add that I consider it bad form to downvote my answer, as there was no information available when I posted this answer on whether your bootloader was unlocked or not.