I'd like to be able to control the distance where the tooltip is placed. I searched through the props, style classes, and also here in the Github issues but I didn't find anything that was easy to configure to achieve this:

I tried some hacks around marginTop and top, but the component recalculates its position based on them so it's ineffective.
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Using the padding/margin is the right direction to take.
Can you please clarify how exactly?
https://codesandbox.io/s/modest-solomon-qjxqk
This is left to be answered on StackOverflow.
This really should be better explained in the documentation.
In case anyone is looking for the solution, here it is:
const useTooltipStyles = makeStyles(() => ({
tooltip: {
margin: 0,
},
}));
const classes = useTooltipStyles();
<Tooltip
title="Tooltip Text"
classes={classes}
>
<button>Tooltip Test</button>
</Tooltip>
Unfortunately if you have an arrow, you'll need to calculate that height into the margin so the arrow doesn't sit over the anchor element.
@zeckdude Thanks for your answer. This is working. But when I tried to override in MUI theme's tooltip options it didn't work.
MuiTooltip: {
tooltip: {
margin: 0,
},
},
I'm not using arrow