"We didn't ask for that"
As SM, these claims would raise a red flag for me. Something is going wrong with the communication and/or the Scrum implementation. They could be a good reason to start doing retrospectives at the end of every sprint and discuss these matters.
If you are doing professional Scrum, events should give you enough opportunities to perform control checks along the sprints.
If you aren't doing professional Scrum, it's an opportunity to learn about the framework, the SM role and bring these issues to the table yourself and get the whole team involved because the solution cannot depend on a single person.
Back to the core question, you could add a CHANGELOG.md file to the source code. Something along the lines of this1, but enriched with issues' ID, sprint goals and number, etc.
The alternative is placing this information as SCM comments. Some SCMs allow links to issue trackers (Jira, Redmine, Asana, etc.). However, I don't think SCMs can give you the best support to format and search the information as you need it.
The advantage of the changelog file over comments is, essentially, the format. It's plain text. You can format it and arrange the info as deemed best. SCM's text searches will complement the results (files with code) with literature (changelog's entries).
Also is a single "file-to-go" vs "go the issue tracker, then the SCM and then the source code".
Side note: This Changelog file is not supposed to be public as those we see in public SCMs or Official websites. Not even for stakeholders. The only audience of the file is the Scrum team. More specifically, for developers.
1:Only for illustration or guidance. Adapt the format, the content and the literature to the needs of the team.