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In short:

The supervisor's edit is ungrammatical because it uses two Determiners within the same immediate noun phrase. As shown below, this is ungrammatical in modern English:

• *the my car

The full story:

1. the slimey dinosaurs

Noun phrases come in two chunks. They have a Determiner and a Head. In (1) above, the Determiner is the word the, and the Head is the phrase slimey dinosaurs.

The Determiner function is a grammatical relation. In other words, the term Determiner describes a job that a phrase or word carries out in a sentence. Examples of other functions are Subject, Object, Predicative Complement and so forth.

In the same way that Subjects are very often noun phrases, the Determiner function is very often carried out by a class of words called determinatives. These include words such as a, the, some,this, that, no and so forth:

2. a/the/some/any/no dinosaur

However, in the same way many other types of word, phrase and clause can function as Subjects, other types of word and phrase can be Determiners. Of particular concern to us here, genitive pronouns and other genitive noun phrases can appear in Determiner function:

3. [my] dinosaur - ^{genitive pronoun}

4. [that man's] dinosaur - ^{genitive noun phrase}

Now the pertinent rule relating to the original poster's question is that standard English will only allow one Determiner in any given noun phrase. Examples (5—8) below are therefore ungrammatical:

5. *the my dinosaur
6. *any her dinosaurs
7. *no those people
8. *a John's friend

The Original Poster's Question

The Original Poster's noun phrase was:

(9) Kukhtarev's model

Here we see the genitive noun phrase (NP) Kukhtarev's in Determiner fnction within the larger NP. This is exactly analagous to:

(10) John's car

Now it is possible that the supervisor was aiming to change this to:

(11) the [Kukhtarev model]

Here, in (11), the word the is in Determiner function and Kukhtarev in contrast appears a modifier within the Head of the larger NP. The three possibilities here are that the supervisor did not notice the 's, that the supervisor made an incomplete edit and failed to delete the 's, or that the supervisor's knowledge of English is incomplete. We cannot know. In any case the resulting string after the edit is categorically ungrammatical because it has two Determiners in the one NP:

12. [the] [Kukhtarev's] model

Likewise so is the following:

13. [the] [John's] car

If we wanted to use both a definite article and a genitive noun phrase we could use an oblique genitive construction to correct these:

14. the model of Kukhtarev's ...
15. the car of Johns' ...

Lastly, to avoid confusion, and before anyone asks, there is one situation where we might see the word the followed by a word like Johns' or Smiths'. This is where the Determiner is a plural genitive noun phrase:

16. [the Smiths'] car
17. [the Johns'] car

In (16—17), the word the is not a Determiner within the larger noun phrase. Rather it appears within the smaller Determiner noun phrase as shown. In (16) we might be talking about a car belonging to Mr & Mrs Smith and similarly for (17) a car belonging to Mr & Mrs John. We can't use a definite article when we refer to a singular person using a proper noun like this. The reason is that we don't use articles when using a singular referential proper noun:

18. *The John punched me - ungrammatical

If the word John were not a name, but a common noun, for example the venacular for a toilet, or a prositute's client (as mentioned by @Weather Vane), then there would be no problem with noun phrases like the following:

19. [The john's] door was wide open.
20. [The john's] car was parked outside.

In conclusion: the Original Poster needs to stick to their guns.