E 120 or carmine is a pigment or a red colour obtained by crushing cochineal insects. It is not a secretion of the insect, but rather it is the body part of the insect. The food industry use it because it is a natural colour that meet food regulation standards of most countries of the world. Besides it is a colour that is known as the best ‘’natural colour’’ that may be consumed.
(refer to hadith of Abu Dawood)

Allah Ta`ala has said in the holy Qur-aan: ‘’(And Allah) makes lawful for them good things, and makes unlawful for them impure things.(7:157) Impure things are food considered as ‘’disgusting’’ according to fuqaha during the best of era: Sahabas and the two generations after them. Because these were the closest to the beloved prophet SAW.

Between the list of ‘’impure things’’ we find insects also. In fact the beloved prophet SAW used to open old dates to enquire whether they had insects or not.
عَنْ أَنَسِ بْنِ مَالِكٍ
قَالَ أُتِيَ النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ بِتَمْرٍ عَتِيقٍ فَجَعَلَ يُفَتِّشُهُ يُخْرِجُ السُّوسَ مِنْهُ
ابو داود

Hazrat Annas r.a. says that when the beloved prophet SAW was brought old dates, then he used to open enquiring for insects inside the dates. Then he would take out the insect from inside the dates to eat it. (Abu Dawood)

This is a clear proof that we should avoid all food contain insects, even those that contain ants.

As such it is not permissible to consume E 120 as such.

Note that E 120 is present in a lot of food products. Including lots of juices, confectioneries, ice creams, chewing gums, etc. Some of them are manufactured by Saudia Arabia, Malaysia, Egypt and muslim countries. So you need to read ingredients before eating or drinking anything. There is a need to follow the sunnah of enquiring before eating anything on the market (refer to hadith of Abu Dawood).

HUJJAAJ SHOULD BE AWARE THAT SOME FOOD AND DRINK PRODUCTS AVAILABLE IN SAUDI SUPERMARKETS DO CONTAIN E 120/CARMINE. SO DO READ INGREDIENTS ESPECIALLY STRAWBERRY FLAVOURED MILK AND CONFECTIONARIES.

Note that fuqaha found that carmine is tolerable in non food or cosmetic products since insects are pure and paak on the skin. And also it is halaal for trade.