By default, HubSpot will use Twitter cards whenever a link is inserted into a Twitter message.
Twitter cards show an image and then a link preview below that. The image is automatically chosen by Twitter based on the OG tags of the link being shared. Twitter does not allow users to change the image associated with a twitter card.
If you'd like to change the image, you will want to click the insert image icon which will expose additional image options but will also remove the link preview (as shown below):