Change structure of block content
If you are not in control of the initial building of the content then hook_block_view_alter() can alter the content of any block before it is rendered.

From the API page:

Perform alterations to the content of a block.

This hook allows you to modify any data returned by hook_block_view().



To target a specific block...

In hook_block_info(), each block your module provides is given a unique identifier referred to as "delta" (the array key in the return value). Delta values only need to be unique within your module.

The variable $block is passed into hook_block_view_alter(). This variable is defined as:

$block: The block object, as loaded from the database, having the main properties:


module: The name of the module that defined the block.
delta: The unique identifier for the block within that module, as defined in hook_block_info().


So you can check what the module and delta of the block to target specific blocks.