On my iMac the delete key on my bluetooth keyboard is not responding.

Is that an Apple Magic keyboard that came with the iMac? If so, does the Delete key work if you plug the keyboard into the Mac with the charging cable that it shipped with?

Have you restarted your Mac lately?

If a simple reboot of your Mac doesn’t fix things, see if the problem still happens in safe mode.

How to use safe mode on your Mac - Apple Support 

Safe mode will often correct weird software behavior by forcing the OS to do disk repair, clear caches and other housekeeping and temporarily disables third-party mods. When you're in safe boot, the machine won’t be at its best performance, especially with graphics, but that's expected.

Does the same thing happen while in Safe mode?

You can exit safe mode by restarting your Mac normally.

Can you test that keyboard with another Mac?

Are you running any sort of anti-virus, cleaning, optimizing or VPN software? Apps of these types often interfere with the proper operation of the OS. If so, try disabling them and see if that has any effect on the issue.

You might also please run an EtreCheck evaluation of your Mac and post the generated report back here in a reply. EtreCheck is a safe and highly regarded utility from a trusted developer and respected ASC contributor. The diagnostic report will not include any personal info. It simply gathers specifics about hardware performance and installed software that might be in conflict with the OS. The report will give us clues without having to play twenty questions.

Please navigate to EtreCheck.com and download the free version. Be sure to Allow Full Disk Access when you install the app. Once you’ve run the app and created your report please post it with your reply to this message. 

Please note you must upload the full report. To see how, please click >  How to use Add Text when posting… EtreCheck Report.

We’ll use your EtreCheck report to look for the things that may be causing your problem and advise how to correct them.

Please download and run Etrecheck.  The free version is sufficient.

Copy the report as shown in this animated screenshot

and use the Additional Text button to paste the report in your reply.

Then we can examine the report and see if we can determine the cause of the problem.

It didn't make it. Here's how to copy and post it:

Copy the report as shown in this animated screenshot

and use the Additional Text button to paste the report in your reply.

Then we can examine the report and see if we can determine the cause of the problem.

Sorry, no, your report still didn't get pasted. 😔

After you copy the report as in the guidance given above by @Old Toad, click Reply here in the thread.

Then click the "Additional text" icon at the bottom of the Reply window and do this: