@bdb484's answer is good and correct. I'm coming in with the advantage of its commentary to address the questions generated there; this is just too long for a comment.
I own a kitchen knife. I can do with it as I please - carving a turkey for dinner, opening packages, throwing it at a dart board, or throwing it away.
One day, I use that kitchen knife to kill someone. Killing people is illegal (generally). Since I've used the knife to commit a crime, the knife is now physical evidence. If I move the knife, throw it away, melt it down, or possibly even run it through the dishwasher, I've destroyed, mutilated, concealed, removed, or altered physical evidence, almost certainly with the "intent to impair its verity or availability in the pending or prospective official proceeding".
Thus, after I've murdered someone with the knife, I can no longer legally dispose of it (etc.) even though I still own it. The knife is no longer merely property, it is also physical evidence. Since it is now physical evidence, this law comes into play and it's illegal for me to take advantage of the normal rights I have to my property.
The police investigating the murder have the right to remove the knife as a routine part of the investigatory process. Their removal (and any subsequent alterations; eg., removing some of the blood to run tests) would be done without "intent to impair its verity or availability in the pending or prospective official proceeding" - in fact, their removal (etc.) is done with the specific intent to maintain its verity and availability. So, their actions are legal under this law.
So, we've got 2/3 of the law handled: I can't destroy the knife since I would be doing so to impair its availability, and the police can remove the knife from the crime scene because they're doing so without intending to impair its availability. Why, then, does the "acting without legal right or authority" clause exist?
I can see four categories of reasons for the "legal right or authority" clause:
First, as a broad clause that allows "weird" situations to be handled without jumping through too many hoops. Consider a suit that alleges that all of the evidence bags manufactured by Brand X between dates Y and Z were somehow tainted by the manufacturer (see, eg., the Phantom of Heilbronn, where a cotton swab factory's swabs were contaminated leading to police thinking they had a prolific serial killer on their hands) and a judge ordered that all evidence in those bags be destroyed. Lucky for me, my knife was in one of those bags and a police tech of some sort is going to destroy my knife. Are they acting "with intent to impair its verity or availability"? Probably, actually, since the judge's order was to destroy the evidence so that it couldn't be used. But, that doesn't matter: they're acting with the legal right or authority to destroy the evidence, so they're not committing a crime under this law.
Second, to allow evidence lockers to be cleaned up. If I've been found guilty and am out of appeals, is there any value in keeping my knife in an evidence locker somewhere? What if I've died? What if I died 100 years ago? If there are clear and reasonable policies for the destruction of evidence that can no longer be reasonably required, is the person destroying said evidence acting "with intent to impair its verity or availability"? It doesn't matter: they're acting with the legal right or authority to do so.
Third, to handle evidence which is dangerous to collect or store. This could include explosive devices, drugs, etc.. My brother-in-law had a summer job destroying seized pills (alleged prescription drugs) for the local police department (which included a lot of paperwork and cross-sign-offs). Bomb squads intentionally detonate explosive devices. Do those people act "with intent to impair its verity or availability"? Again, it doesn't matter: they've got the legal right and authority to do so.
Fourth, to handle legitimate mistakes by those in custody of the knife. I grant that this is the weakest reason, though. If I've (illegally!) washed the blood off of my knife before the police take it, consider the lab tech who scrapes off the tiny bit that I missed to run various tests on said blood (legal due to no intent to "impair its verity or availability"), then trips and drops the vial with the bit of blood in it. Did they destroy the evidence with the intent to impair its availability? Probably not, but they had the legal right and authority to do what they were doing and the trip was accidental; they shouldn't be guilty of a felony for stumbling in the lab.
Therefore, all three clauses are necessary for the law to have its desired effects:
- I lose property rights when my knife becomes physical evidence
- the investigators gain a number of rights to my knife when it becomes physical evidence
- there are mechanisms by which my knife can still be destroyed or altered with the intent to impair its verity or availability, if appropriate
But, wait, you might say: none of those scenarios should qualify as "with the intent to impair its verity or availability".
There's one more clause to that law which is important to consider:
(b) Knowingly makes, presents, or offers any false or altered physical evidence with intent that it be introduced in the pending or prospective official proceeding.
Consider a "molehunt" or other internal investigation. It may be necessary for false evidence to be introduced to a suspected bad actor, even if the purpose is to see if that evidence is introduced in the official proceeding. Without that "legal right or authority" clause, such an internal investigation may be functionally impossible to conduct. For example, if there's suspicion that a prosecutor is, shall we say, "less than ethical" with regards to where they get their supporting evidence, it may be necessary to provide them with false evidence to prove their wrongdoing when they use that evidence in court. In that case, whoever made and presented the false evidence would be acting with the legal right or authority to do so, so would not be guilty of a felony under this law.