Block Quotes in Scrivener
Block Quotes are sections of text that is indented. For MMD, you simply place the ">" character at the beginning of a paragraph. Unfortunately, Scrivener does not interpret that option and simply ignores it.
Unfortunately, Scrivener doesn't seem to want to interpret this and send it to other filters.
This is simply gathering research pointers to try and solve this problem.
Instead, you can use the ruler (Format>Show Ruler) to adjust the indentation of your current text.
To ensure that compiling doesn't strip that out, you need to preserve the specially formatted text. To do so, select the text and go to Format>Formatting>Preserve Formatting. It'll turn blue with a dashed outline.
There is a Block Quote preset that you can apply to the text, but it may not give you the look you want. If you plan to do this frequently in your text, you can do as I mentioned above, select the preserved text, then go to Format>Formatting>New Preset From Selection. This will allow you to create your own preset that you can use to quickly apply the formatting to other sections of text and ensure they're all formatted the same way.
This article covers presets and preserve formatting too: