" but they let it through to comply with the law."

First let's look at some 'laws' Keith

We'll start with the obvious one which has been discussed here the naval and land blockade

The 1909 Declaration Concerning the Laws of Naval War (the London Declaration), the first international instrument to acknowledge the legality of blockades, specifically recognized the right of belligerents to blockade their enemy during time of war.
Article 97 of the San Remo Manual does likewise

But what justifies a blockade in non-international armed conflict (NIAC)? The London Declaration does not justify such a blockade, because it only applies to "war"– war being understood at the time as armed conflict between two states.

The seeming absence of support for blockades in NIAC is obviously important, because it is difficult to argue that Israel is involved in an IAC with Hamas.

First, it is obviously not in a traditional IAC, because Gaza is not a state.
Second, not even Israel claims that the conflict has been internationalized by the involvement of another state.
And third, although the Israeli Supreme Court held — controversially — in the Targeted Killings case that armed conflict between an occupying power and a rebel group is international, Israel's official position is that it not currently occupying Gaza.

Insofar as Israel insists that it is not currently occupying Gaza, it cannot plausibly claim that it is involved in an IAC with Hamas. And if it is not currently involved in an IAC with Hamas, it is difficult to see how it can legally justify the blockade of Gaza.

Its blockade of Gaza, therefore, seems to depend on its willingness to concede that it is occupying Gaza and is thus in an IAC with Hamas.

But Israel does not want to do that, because it would then be bound by the very restrictive rules of belligerent occupation in the Fourth Geneva Convention

As an occupying power that exercises effective control over Gaza, Israel has legal obligations to the residents of the occupied territory under the Fourth Geneva Convention, including the general duty to protect civilians under its control, and the specific duty to allow adequate access to food and medical supplies

Israel's claim that its occupation of Gaza ended with its 2005 withdrawal of troops and settlers from the Strip is an attempt to absolve itself of responsibility for Gazan civilians.
The continued control of Gaza's territorial waters, its airspace, the flow of people and goods through its land borders, and its continued ground and air incursions into the territory, verify that it exercises the "effective control" necessary to qualify as a foreign occupying power under the Fourth Geneva Convention.

Even if the Gaza Strip were not occupied, Israel would still be constrained by the principle of proportionality in imposing the blockade.

This means that the military advantage gained must outweigh the harm caused the civilian population.

To comply with the law -

IT MEANS THAT THE BLOCKADE MAY BE NO MORE RESTRICTIVE THAN IS NECESSARY FOR MILITARY PURPOSES !

In other words there is no justification in law whatsoever for the refusal to allow in hundreds of items of food plus batteries for hearing aids, childrens crayons, school books, shoes, musical instruments hair brushes and the many purely arbitary list of banned goods which it took a court case to uncover except to break the spirit of the 1.5 million residents

Israel's stated objective in imposing the blockade is largely not military, but political in nature, namely, to weaken Gaza's economy and decrease support for Hamas.
The damage that the blockade has caused to the civilian population is therefore clearly disproportionate to any military advantage Israel could obtain from the blockade.


Settlements and international law

The consensus view of the international community is that the building of Israeli settlements in the West Bank, including East Jerusalem, is illegal under international law.

The primary judicial organ of the UN, the International Court of Justice, found the settlements to be illegal under international law.
The Court's finding was based on the provisions of the Fourth Geneva Convention and UN Security council resolutions, which condemned establishment of settlements and attempts by Israel to alter the demographics of the territories under its control.