On what model Mac are you making these recordings? Identify the model of your Apple device - Apple Support
What is the version macOS on that computer? Find out which macOS your Mac is using - Apple Support
To reduce the size (and thereby the quality) of QuickTime screen recording movies, you would have to re-encode the existing movie at lower quality. Depending on how powerful the Mac is, that may take some time. HandBrake is a often recommended tool for re-encoding movies with different parameters.
For any movie (every source) this is true: file size = bitrate × duration. Duration is simple: shorter movie clips are smaller in size, and near-linearly. Bitrate is a combination of frame size, frame rate, and codec efficiency. While bitrate is often not exactly constant, it is quite predictable with averages. Most users want to keep frame rate as-is, or else you loose fluid motion. For codec efficiency, H.265 HEVC creates smaller movies than H.264 AVC — if the playback device is compatible.
Audio is very compact compared to video, so don’t worry about that too much, although you can save a bit there as well, if you must.
To give more concrete advise, please answer these:
- How long (runtime) are your typical screen recoding movies?
- What size in pixels (width×height) is your screen capture movie? Would scaling down (smaller frame size) be acceptable?
- What size (in bytes) are your movies now? How small do you need them to be? Movie files are big by their nature. Don’t expect email attachment sizes.
- Do you have a special use in mind for these recordings? That would help formulate a ‘best strategy’.
You can also explore other screen recording applications, to see what settings for quality those provide. It would be different, but not necessarily better. I have no advise for that, though. Maybe someone else here does?