Thanks. having a deeper look, I now see my misunderstanding. I was believing that the image was coming from page.content but in face it was above in the theme. If that can interest someone, I have changed in my templates/partials/blog_item.html.Twig file, around line 50 at the time of writing :
{% if big_header %}
{{ page.media.images|first.cropResize(1038,437).html(page.title, page.title, 'image featured') }}
{% else %}
{{ page.media.images|first.cropZoom(1038,437).html(page.title, page.title, 'image featured') }}
{% endif %}
to :
{% if not big_header %}
{{ page.media.images|first.cropResize(1038,437).html(page.title, page.title, 'image featured') }}
{% endif %}
Maybe not the best solution but it works :)