I can assure you that I have never deleted this knowledge to regain it through Annolisa for this group. If it is a quest reward, I can't recall, I would suggest leaving it as high as you can and then perhaps it will upgrade higher on subsequent character playthroughs.

No, it will not upgrade, its rank is rng-based and granted at the moment I speak with npc.

Currently I'm in the middle of another 515-Energy attempt with 300 left, if I'm not getting S this time then its rigged or broken and I quit and taking my money with me. I'm not spending a single cent on this roulette, just look at Steam sales how much I can get for 15$, I can buy new game every month while not being frustrated, disappointed, and anrgy that my several months time and effort went down the drain BeCaUsE iTs ChAnCe-BaSeD tRy YoUr LuCk NeXt TiMe.

Hmmmm.  https://postimg.cc/kVWq6vjJ

Its still rigged. I got what I earned only after threat of quiting.

Congrats ... I'm just trying to get the knowledge to S rank as well. I deleted it with my main character but when talking to Grusha he won't teach me the knowledge.
Now I created a new character and did the main quest up untilk the point where I get the knowledge as a quest reward (rank C). I continued the main quest up until I defeated Giath and deleted the knowledge again. Now I have the same problem as before: Grusha won't teach me the knowledge.
At what point is it possible to delete the knowledge and still be able to learn it again?

You can delete this knowledge as soon as you obtain it, after deleting you can talk to Grusha to get the knowledge again, possibly at different rank.
You need to choose correct Crossroad path during questline, though.

Since the problem still has not been fixed by now, I'm posting an alternative solution to this problem that is way more afk than the endless repeating of Balenos questline, that is IF you have any alts to spare.
All you have to do is get all of the knwoledge in that tab, does not matter if its S,A+ or even C. That also means having the Giath's Secret knwoledge aka. fishing the quest at least once which is not a problem at all. Once you have that go to Calpheon to the same NPC that can remove knowledge for 10 energy. Another option she has for you is making a book for your residence. It will remove some of the knowledge from that tab at random. Seeing as all goblins except the Giath's Secret are pretty much free to get, it's not a big problem. The book you want to make is Bookshelf with Knowledge on Goblins. After that all you have to do is pretty much put it in any residence and use alts to read. It is a 3600s ( 1 hour ) cast that at the end will give you a random knowledge from the Ecology -> Balenos -> Goblins tab. Tab, that includes Giath's Secret. Important thing to note is that :
a.) you can click R to read on an alt and change to any character you want. It will keep reading as long as you are logged in on your account.
b.) you can have unlimited amount of alts reading from the same book at the same time ( I got S in a single day reading with 6 alts ).
c.) while you are free to swap characters, you have to stay on the same server ( ex. Me4 , Ba6, Ody1 )
I do not know if it has any effect of reading, but during my "grind" I used Savage draught and Cron Meal for the "Higher grade knowledge gain chance". It's pretty cheap and time doesnt go down while not on alt, so 1 of each is enough to use.

Thanks for your contribution.

The problem will not be fixed because it is not a bug, it works as intended.

There are several ways to obtaine the knowledge, I always forget we can make alts read books.

Wonder is there is a possibility to gain knowledge on basilist Statue without actually killing it.

Back in my days, I ran groups for quite long time, everybody get the knowledge except me - low AP means less chance to land a killing blow, and only killing blow triggers rng to grant knowledge or not.