Video team sending huge video files and telling you that’s the smallest they can get is common. The smallest is often too big for web. I use this online tool to reduced video size.
How to optimize video for the web
Some people will try with settings in Adobe Media encoder but this website makes it easy.
1) upload
2) resize (or add the same dimension for a “compress” same size version)
3) download the new lighter version
https://ezgif.com/resize-video
For videos up to 100MB, free tool, no watermark added to your videos.
Cut a video
You can also cut a bit of the video (for instance if you want your video to loop but you have a black frame at the end of the video) https://ezgif.com/cut-video
Convert any video to MP4
MP4, WebM, AVI, FLV, MOV, 3GP and other video files
Max file size: 100MB https://ezgif.com/video-to-mp4
Hope that helps.
Cheers,
Denis