Looks a issue of Jenkins core, not parameterized-trigger.
Changed component/s.

Seems to be an issue with Chrome. With IE and Firefox, I am able to save after removing a parameter.

Same issue here with Chrome 34.0.1847.45 and Safari 7.0.3 (9537.75.14).
It works fine in Firefox 25.0.

In step 5, are you reloading the page, or navigating away, then clicking on the 'Configure' link in the sidebar?

Is there a step 6 "Click on Save or Apply" missing in your description?

Are there any JavaScript errors?

Are you trying to click the buttons with the mouse, or do you give them keyboard focus and trigger them by e.g. pressing Space?

Which browsers (+versions) work, which are affected by this issue? Which is the last known good Jenkins version?

Any watchers: Feel free to contribute information here.

If you have a public, affected Jenkins and could open up one job's config page for me (in private, send email) that would be great.

Unfortunately, there's a lot of conflicting information about this – and we haven't even looked at plugins possibly breaking the job config page. FWIW, I cannot reproduce it in Firefox 29, Safari 7, or Chrome 34 on OS X with 1.559 or 1.561.

JENKINS-22582 looks a lot like this, and is fixed in 1.560. Can anyone confirm whether this issue is also fixed?

Let's assume this duplicates JENKINS-22582 and is fixed in 1.560. This issue can always be reopened, or a new issue can be filed, if this still happens in 1.560+.

(Please file a new issue if it happens in versions much newer than 1.560, say 1.580 or higher given that it might be an unrelated issue with the same symptoms)

Although this has been resolved as dupe, I am seeing this in 1.556 (linked bug 22582 is assumed the dupe, but was fixed 1.554). The behavior I see occurs in Safari and Opera on mac, and the behavior described (removing a defined parameter) is one instance that can cause this.

I see a javascript warning in opera, 'event.returnValue is deprecated. Please use the standard event.preventDefault() instead.'

I cannot get your point.
As @danielbeck said, JENKINS-22582 is fixed in 1.560.
And it's not strange Jenkins 1.556 is still affected by that problem.
What tells you JENKINS-21582 is fixed in 1.554?

Erik: The label '1.554.2-fixed' on the linked issue means that the fix was backported to the current line of stable Jenkins releases.

As you can see from the commit linked in the linked issue's comments, it was first included in 1.560.

Thanks Daniel for explaining the backport tag; ikedam, I read the backport tag and assumed that meant the issue was claimed fixed in earlier version, which is why I mentioned my issue.

Looks like this issue is back with 1.569

outspoken: Is that a typo, or are you referring to a >6 months old release?

Typo... Jenkins ver. 1.596

I can get it to work in Safari but Chrome (even Chrome Canary) doesn't work.

Cannot reproduce the issue on a pristine instance of 1.596 with Chrome 39, therefore resolving again. Note that nightly, alpha, beta, or Canary versions of browsers are not supported, see https://wiki.jenkins-ci.org/display/JENKINS/Browser+Compatibility+Matrix

Please read https://wiki.jenkins-ci.org/display/JENKINS/How+to+report+an+issue and file a new issue that can be investigated independently from this one (i.e. let's not spam the watchers), as the problem you're experiencing seems to only occur on some circumstances.