In an attempt to guarantee the security of its innovative water purifi

When you say "prohibit from", the correct form of the idiom is -

"prohibit someone/something from something"

For example -
The court ordered the Bureau of Immigration to prohibit the accused from leaving the country.

Another way in which "prohibit" can be used is "prohibit something"

For example -
Kuwait was the only nation to prohibit the entry of Syrian nationals prior to Trump's executive action
Reddit's rules strictly prohibit revealing anybody's private personal information (Note here that "revealing ..." is a noun).

Let us look at the answer options -

Option A - Incorrect.
"prohibiting that its water purification methods be disclosed to companies" - Note that "prohibit" does not take the command subjunctive.

Option B - Incorrect.
"them" is incorrect. "each employee" is singular.

Option C - Correct.
This uses the second form of the idiom - "prohibit X"
X = the noun phrase "disclosure of its water purification methods to any company"

Option D - Incorrect.
"that would prohibit them from disclosure of its water purification methods to companies"

"them" is incorrect as "each employee" requires a singular pronoun.
"prohibit X from doing Y" is the correct idiom. "disclosing" should be used instead of "disclosure".
"would prohibit" - uses future in the past form "would". Implies that prohibition occurs some time after "signing". Illogical. Employees are prohibited from disclosing information as soon as they sign the agreement.

Option E - Incorrect.
Note that "prohibit + infinitive (to + Verb)" is not idiomatic.
"that would prohibit" is incorrect.

Hope this helps