Let me address the weirdness of situations like this:
This would appear to be a situation where someone (possibly mistakenly, but likely deliberately) misused the scoring tool to mark several points inside White’s territory as “dame” points (as indicated by blue squares), which significantly reduces White’s score and possibly changes the outcome of the game.
One easy solution (as suggested by @stone.defender) is to just completely disallow dame to be marked inside of apparent territory. However, this would negate what I believe is its primary function, that is, allowing players to mark teire points left due to unfilled dame.
To explain let me use some examples from another post, where I discussed some of the intricacies of dame filling.
Under formal application of the Japanese rules, player are compelled to fill in dame points to prevent technical sekis. Of course, in practice, with casual play and most games on this site, players will often leave some dame unfilled, even sometimes when those dame kind of matter.
A basic example
Here is a simple example that we often see in OGS games that have gone to scoring:
The dame at A has been left unfilled, which has allowed Black to avoid defending B. Formal application of the Japanese rules requires both players to play another move (White at A and Black at B), however, players on OGS often skip these additional two rules as a shortcut. Hence, to properly score the above situation, the blue square feature should used to mark both A and B as neutral.
Some other examples
Teire points that should be marked as neutral can become more complex than that.
In the below two examples, there are no more urgent moves left to play, and conceivably the players might choose to pass early before filling in the remaining dame or fixing the teire. In both cases, the white stones marked with X are dead. Let’s consider how one might try to score these positions, if both players simply decided to pass instead of playing out the dame filling and teire.
In this first case, the two points at 2 and 4 should be marked with the blue squares, since Black would have been compelled to fill those in response to White filling dame at 1 and 3.
The White stones marked with X are dead and the points underneath them should count as territory for Black. However, would the scoring system properly count those points as territory (given that they are only adjacent to points marked as neutral with a blue square)?
In the second case below, the point at 2 should be marked with a blue square, since Black would be eventually compelled to fill at 2.
The white stone marked with an X is again dead here, but since Black should eventually be compelled to fill that as well (in order to connect, in response to White filling the dame at 1 and 3), the point under that dead stone should not be counted as territory for Black. However, can the scoring system mark the White stone as dead, but also the space underneath as non-territory for Black?
Hence, if the players take the shortcut of not playing out the dame filling in the last two cases, I’m uncertain if it is even possible to score the games correctly. Of course, in all of the above cases, the simple way to avoid any issues is to simply play out the dame filling, which would obviate the need to mark points with blue squares and worry about which points are counted as territory.