Is there any hook for a tag page, so I can alter it's content before outputting?
There is a conditional called :
//From the codex
Archive pages are not generated by some specific function, but are produced by processing template file from your theme.
For tag archive page see Template Hierarchy > Tag display to determine which file in your theme could be it.
If theme you are using comes from official repository and likely to be updated it's good practice to create Child Theme for it, so that your tweaks survive update.