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The process for eliminating invalid code points within a string depends on the specific programming language, as well as the context in which the string is being used. However, some general steps that can be taken include:

1. Determine the acceptable range of code points: The first step is to define the range of valid code points for the given context. For example, in a string that represents ASCII characters only, any code points outside the range of 0-127 would be considered invalid.

2. Identify invalid code points: Next, the string should be scanned to identify any code points that fall outside the acceptable range. Most programming languages provide utility functions and libraries for this purpose.

3. Remove or replace invalid code points: Once the invalid code points have been identified, they can either be removed entirely, or replaced with valid alternatives. For example, if a string contains non-ASCII characters and needs to be converted to ASCII, the non-ASCII characters can be replaced with their closest ASCII equivalents (e.g. é becomes e).

4. Re-encode the string: Finally, the modified string may need to be re-encoded in a different character encoding to ensure that it can be properly handled by the system or application where it will be used.

Overall, the process for eliminating invalid code points requires careful attention to the specific context of the string, as well as a strong understanding of the programming language, character encodings, and related concepts.