Is it permissible to open a trust to remove its indecent cover before delivering it to the addressee, or is that considered a violation of the trust?

If the picture is on the garment's cover, it can be blurred in a way that does not damage the garment, based on the hadith (definition) of Ali (may Allah be pleased with him) that the Prophet (peace be upon him) commanded him to blur statues and pictures.

However, if the cover is merely a bag, the item can be placed in another container without a picture. If a greater harm is feared, then the item should be given to its owner as is, and she should be asked to blur the picture herself.