Dips which were used before Pesach are highly likely have actual chametz in them which aren’t nullified so these you must get rid of. If you know there is chametz you must get rid of it. If you are not sure then you need to check it and see if there are actual crumbs. If there are none ten you can keep it over Pesach. It is better to put it in a bag and label it chametz.
Explanation:
The Mishna in Pesachim 42a: These are the things which you are not allowed to keep around on Pesach, Kutah HaBavli, Medean beer, Edomite vinegar…
These are things which have Chametz mixed into them, which Rashi explains meaning they transgress Bal Yeraeh.
The Rishonim argue whether the Mishna is only talking about foods that have a Kazayit of chametz which can be eaten in Kdei Achilat Peras. Or even if it has a Kazayit spread out even thinner.
Rabbeinu Dovid, the Ran, Mahram Chalava explains Rashi that one transgresses even if it less then Kdei Achilat Peras. The Maggid Mishna explains Rambam as needing a shiur. The Kesef Mishna argues that the Rambam agrees to Rashi.
The Chatam Sofer explains the Maggid Mishna that if there is no Kazayit kdei Achilat peras the Chametz is considered nullified in the mixture enough that you do not transgress bal yeraeh. Even if you say that it is not possible to have ‘Bitul’ for Bal Yeraeh, the issur of eating Chametz is not on chametz which is permitted to eat you do not transgress Bal Yeraeh. (This is based on the opinion of the Ran that Bal Yeraeh is based on that you might come to eat chametz if you find it. )
The Shulchan Aruch 447:1 writes if chametz gets mixed not something before Pesach and it is less than 1/60 it can not be considered in existence to make it forbidden on Peach, some argue.
The Rema writes: we follow the first opinion by liquid mixtures however by dry mixtures or if you are concerned about read falling into wine it is forbidden to eat on Pesach even if you take out the bread because we are worried about crumbs giving the food flavor on Pesach.
The Shulchan Aruch rules that the chametz stays nullified, and the Rema rules that by liquid it is not forbidden, however by dry mixtures it is.
The Mishna Berura say that Rema is stringent if you are going to eat it but it’s permitted to derive benefit and permitted to keep it around since it only a worry.
The Chazon Ish (OH 119:12) writes that it is even forbidden to derive benefit or to keep it around. He also writes even if you don’t transgress Bal Yeraeh since it does not have any chametz but we are required to destroy all things we can’t eat because of chametz by bedikat chametz.
According to the Rema we have a question whether it is even permitted to keep it around, but according to Shulchan Aruch it is even permitted to eat it and especially to keep it around.
Even though the Shulchan Aruch in 442:4 sounds like he is stringent he the chametz does come back on pesach, : Something which chametz was mixed into and it is not edible at all or even not edible to some people even if it’s permitted to keep it around you cannot eat it ;until after Peach.
The Mishna Berura explains that it got mixed in before Pesach.
The Chazon Ish explains, in 442 he mixes it in on purpose before Pesach so we say that it became forbidden on pesach but in 447 it got mixed in accidentally the foe it stays nullified.
Any way you are allowed to keep it around in either case.
In conclusion we can keep around hummus which was eaten with chametz before Peach. If you see crumbs you must take them out and even after we have to be nervous that some crumbs are left they are nullified and don’t return therefore it permitted to keep it around.
