Neither: instead, change the target of the negation
Because "used to" is an idiomatic expression which does not, otherwise, reflect current usage over the verb "use" except when used atomically as such an expression (see @JavaLatte's excellent answer, including for the appropriate direct negation form), my usual recommendation is to avoid the controversy between whether or not to change the tense and instead to change the structuring:
Didn't used to get
Used to not get
This is also, in a sense, more overall correct. While "use" is a verb, in its idiomatic form it is not actually the main verb of the sentence. Instead, "get" is. "Used to" is instead an adverbial time marker that stands in for, essentially "in the past." It sets when they did or did not "get." So the negation applying to "get" is more appropriate.
In the past they did not get it.
Didn't in the past get it.
Hopefully the awkwardness if not outright incorrectness of the second phrasing by comparison to the first becomes more immediately apparent when using something other than the "used to" idiom. Personally, I find "didn't used to" along with "didn't used to" to both be similarly awkward, regardless of which one might be regarded as correct.
With this recommendation, the sentence would have improved in overall clarity:
That's money in their pockets that they used to not get.
I would also agree with the portion of @JavaLatte's answer covering "used not to," as it is definitely preferable to my ear and sense of structure than either of the forms using "didn't" if the intent is to negate the sense of past tense rather than the main verb of the sentence. But the related structuring is also, by degrees, relatively more archaic in tone.