They jumped on this pretty quick
https://www.snopes.com/fact-check/obama-foundation-floyd-death/
This rumor has no truth to it. The Obama Foundation’s tweets shared links to its website, Obama.org. The preview image for that page updates dynamically on Twitter when the platform’s web crawlers (bots) re-index (restructure the website data for) the preview image for the website every week.
In other words, at a certain point following Floyd’s death the foundation changed the Twitter Card image for the website, which retroactively updated the image on past tweets. A Twitter spokesperson told Snopes that the image shown in the card updates when the foundation updates the data used to generate the card. The group did not edit the tweet, according to the spokesperson, but may have changed the data associated with the link.
We reached out to the Obama Foundation to ask about the photo on June 8. On June 9, the image from the May 16 post had been changed to the foundation’s logo:
An Obama Foundation spokesperson confirmed for us that the rumor is false, and that the preview image for Obama.org updates dynamically based on information set in the link. The photograph of the poster with Floyd’s face on it was taken on May 30, 2020, according to the foundation, and was first used on the site on May 31.
We therefore rate this claim as “False.”