Nothing really, but that's because the "Jutes" as a distinct ethnic identity that settled portions of England exclusively never really existed to begin with.

The Venerable Bede tells us in his history of the English People and Church that different tribes from continental Europe came to England to make their homes and that certain parts of the country were settled by certain tribes, the Angles, Jutes, and Saxons, hence names like West Saxons, East Anglians, and so on. This is the view that has come down through history and is widely repeated in less academic writings on the subject. Only this isn't how it happened, and modern scholarship has harshly critiqued the old views on the subject of the Anglo-Saxon migration New interpretations of the limited literary evidence and archaeological sources have changed how historians view this time in history.

Robin Fleming talks about how the "Anglo-Saxon migration" was really a broader movement of North Sea adjacent peoples into Roman Britain. This included people from Denmark (Jutland), and Northern Germany (Saxony), but also people from Norway, Ireland, and Sweden. This is because the ethnic groups that lived in these areas did not have hard and fast cultural identities that were incompatible and unchanging. Peter Heather in particular has argued that in Late Antiquity the ethnic identities of many "barbarian" peoples were extremely fluid and changed as political and economic circumstances dictated. The idea of the Anglo-Saxons as a purely Germanic culture that drew from particular regions of continental Europe is misguided and not supported by the evidence that we have available through archaeology. Fleming points to the blend of clothing and jewelry styles that emerged following "Anglo-Saxon" migration to Britain as evidence that these two cultures were assimilating into something difference from either that came before. Jewelry patterns that used Roman coins and items as a part of their construction, in a pattern that was similar to Norwegian patterns, worn by the descendants of people who traced their ancestry back to Africa, Italy, or the Low Countries are just one piece of the evidence that shows the tremendous mixture of influences in Roman and post-Roman Britain. New patterns of house construction, clothing, language, and more all give evidence.

Now this gets to another preconceived notion that we often have of this time period, that these various ethnic groups were locked in eternal conflicts and violence with each other. However, this is not a well supported argument! Fleming views this process as more or less a peaceful one. While there was some endemic violence inherent to the time period, she does not see evidence for the mass violence that is often assumed to have accompanied the Germanic migration into Britain. The idea that the newcomers, be they Angle, Saxon, Pict, or Irish, waded through Roman blood to carve out new kingdoms on the island of Britain that were derived of singular ethnic groups is entirely false.

One thing that is paramount to remember is that these various tribal groups and "peoples" did not form coherent national identities that were set in stone and unchanging. This view of the angles, saxons, and jutes, forming one coherent polity and the British another, oversimplifies the situation to an extreme degree and is an unfortunate holdover of the 19th Century.

So the Saxons of Saxony and the Saxons who settled in Britannia might both speak the same language, worship the same gods, and so on, but they did not necessarily view themselves as the same "people" in an abstract sense of the word. Instead of kinship among these disparate groups of people, we should instead see loyalty between the armed retainers of a warlord/chieftain/insert your preferred noun here/ as the most paramount social identity. Status and position as an armed retained, a precursor to the later Huskarls and Housecarls, were much more important that subscribing to an identity of being "Saxon" "Anglish" or "Jutish".

It was only later on in the Medieval period, as the anarchic period of post-Roman rule stabilized and the centers of British power started to coalesce into states that the ethnic identities of the invaders and the native inhabitants became a powerful tool of propaganda. Robin Fleming argues that the new elite of the emerging states created narratives of ethnic migration as a means to legitimize their rule over portions of the Island, and that the ethnic descriptors of "Angles" and so on came about as a result of political propaganda, not as a stubborn remnant of pre-migration identity.