This petition was rejected

The Government e-Petitions Team gave the following reason:

We can't accept this petition because it asks for something that neither the House of Commons nor the Government can do.

The expression "vote of no confidence" is used when talking about a vote in the House of Commons which tests whether or not the Government of the day has the confidence of a majority of MPs in the House of Commons. That's why we allow petitions asking for a vote of no confidence in the Government or in individual Ministers. The concept of the House having “confidence” in someone does not apply to backbench or Opposition Members.

The resignation of an MP is a decision for that individual, not for the House of Commons as a whole.