How does ATC deal with a crew who is not capable of a clear pronunciation?
There is special phraseology snippets that allow information to be transmitted over the frequency with more accuracy, slower, repeated or worded differently.
ATC may also query other company traffic to relay information in another language or they might use the ACARS/CPDLC system to transmit a text message, should both parties be capable.

SAY AGAIN
„Repeat all, or the following part, of your last transmission“

(Source: AIP Germany GEN 3.4)

WORDS TWICE
„Request: Communication is difficult. Please send every word, or group of words, twice.
Information: Since communication is difficult, every word, or group of words, in this message
will be sent twice.“

(Source: AIP Germany GEN 3.4)

SPEAK SLOWER
„Reduce your rate of speech“

(Source: AIP Germany GEN 3.4)