after refind boots, this menu appears.
do I manage it with efibootmgr OR ?
Thats your GRUB menu. It’s where you decide which os you want to load, and also gives you a shell to fix things or pass kernel paramaters. It does essentially the same thing as refind so if you don’t want to see it, i suspect you manage that in refind. Maybe direct refind straight to your root partition?
my hope was to learn how to eliminate some of the entries – leaving the ones I wish to keep
That’s not the Grub menu. It’s systemd-boot’s menu.
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EDIT!: this was wrong please ignore 
There’s a package called grub-customizer in the arch repository that automates it for you. If you don’t need the things on the list, you can delete them and update grub.
OP is not using GRUB. The menu you are seeing is systemd-boot’s menu.
nvm I was mistaken, its the systemd menu apparently, and I’ve never used systemd so can’t help you. Its supposed to be easily configurable
yeah i just saw your correction. looked just like grub to me - i’ve never used systemd
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You don’t need to install another boot manager on top of what you already have to configure/maintain it. Refer to systemd-boot’s article in Archwiki, to see how it is installed, whereto and where its configuration files are.
efibootmgr will get rid of a lot of that garbage, won’t it?
efibootmgr can manage the paths to bootloaders’ efi binaries in Bios.
What is show in the menu in the op are managed by other config files, normaly under /efi (in EOS case).
It may be the case that OP has things in the Bios that may need attention too but systemd-boot’s menu entries are not managed by efibootmgr.
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This would at first glance appear to be a redundancy.
(That is you have reFind booting first, then systemd-boot, for a total of 2 boot managers.)
A bit like this thread over here:
BUT I also remember that in the past sometimes something like this was necessary due to funky BIOS (see: macbooks) .. where ReFind would chainload the other necessary things.
I find this to be highly unlikely to be the case for you, but thought it worth mentioning.
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Above is the correct answer to my original post?
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Yes.
You didn’t need to install a second boot manager to manage and configure the first you already had. Installing refind, was unnecessary.
Then you need to look at that article where you can read about your first boot manager in order to be able to manage and configure it.
If your objective is to eliminate some of the entries in that boot menu, you need to remove the configuration files for those. They should be found in your ESP. Where this is mounted may differ between the distros you have. In EOS it is at /efi.