Source: Michael Fishbane's Biblical Interpretation in Ancient Israel (New York: Oxford, 1988) 175.
Here's Exodus 22:20-27. I've colored in blue the most important verses for this discussion, and in red what Fishbane deems to be a later addition:
"20 Whoever sacrifices to any god, other than the LORD alone, shall be devoted to destruction.
"21 You shall not wrong or oppress a resident alien, for you were aliens in the land of Egypt.
"22 You shall not abuse any widow or orphan.
"23 If you do abuse them, when they cry out to me, I will surely heed their cry;
"24 my wrath will burn, and I will kill you with the sword, and your wives shall become widows and your children orphans.
"25 If you lend money to my people, to the poor among you, you shall not deal with them as a creditor; you shall not exact interest from them.
"26 If you take your neighbor's cloak in pawn, you shall restore it before the sun goes down;
"27 for it may be your neighbor's only clothing to use as cover; in what else shall that person sleep? And if your neighbor cries out to me, I will listen, for I am compassionate" (NRSV).
Here's Deuteronomy 24:10-18, which Fishbane believes is based on Exodus 22:20-27:
"10 When you make your neighbor a loan of any kind, you shall not go into the house to take the pledge.
"11 You shall wait outside, while the person to whom you are making the loan brings the pledge out to you.
"12 If the person is poor, you shall not sleep in the garment given you as the pledge.
"13 You shall give the pledge back by sunset, so that your neighbor may sleep in the cloak and bless you; and it will be to your credit before the LORD your God.
"14 You shall not withhold the wages of poor and needy laborers, whether other Israelites or aliens who reside in your land in one of your towns.
"15 You shall pay them their wages daily before sunset, because they are poor and their livelihood depends on them; otherwise they might cry to the LORD against you, and you would incur guilt.
"16 Parents shall not be put to death for their children, nor shall children be put to death for their parents; only for their own crimes may persons be put to death.
"17 You shall not deprive a resident alien or an orphan of justice; you shall not take a widow's garment in pledge.
"18 Remember that you were a slave in Egypt and the LORD your God redeemed you from there; therefore I command you to do this."
According to Fishbane, we see a similarity between the two passages. Both discuss loans, right before telling the Israelites not to take a brother's coat as a pledge.
For Fishbane, Deuteronomy was working with the version of Exodus 22:25 that lacked the red part. Deuteronomy does not talk about interest, but it offers its own explanation of how to make a proper loan: do not go into a house to take a pledge.
Does this necessarily follow, however? Deuteronomy 24 doesn't present every law in the same order that Exodus 22 does, so perhaps its author was flexible. He chose not to quote the part about interest, for he wanted to focus on not entering a house to take a pledge.
Was Deuteronomy 24 even interpreting or interacting with Exodus 22? Maybe. I don't know. I have a hard time believing both have loans laws in the same order by sheer coincidence. But maybe they were clustered together in the cultural repertoire, meaning Deuteronomy 24's author may not have had Exodus 22 in mind.