How do I set a controller for my homepage
Ok, maybe you can check if the entry in the matrix block is still valid (non-expired) and if that's not the case, just don't render the matrix block? Put everything in a simple if statement?

Something like this (hasn't been tested, use it as an example of what the actual code would be):

{% for block in entry.myMatrixField %}
    {% if block.type == "something" %}
        {% if block.entry.status != 'expired' %}
            {{ block.entry.title}}
        {% endif %}
    {% endif %}
{% endfor %}