How Can I Append Inline Style to Post Images in WordPress

Simple problem, not sure where to start.

Posts on our website get pulled into an RSS feed and get automatically emailed by an email service. This works perfectly great, except for one thing — normal web size images make our emailed posts look bad on mobile — the images render too big and make the email too wide, such that the text reduces to a smaller size.

I need to add an inline style to uploaded post images:

style="max-width: 100px; max-height: auto;" 

This forces any image to be restricted to the width of the div into which we put the content.

I don’t care if the style tag gets added to the images in the post on the website or in the RSS feed, but it needs to be there or it ruins the emailed post on mobile. When I add the style inline myself, it causes the email look great in a mobile display.

Any thoughts on how I can inject this inline style?