How can this offer be okay?

[Morticia]

I won't be contacting anyone about it ... I understand you can do what you want with your own site but it feels wrong to me especially adding the suggestion to post on review sites in the same email offering a discount. I don't want to belabor the point ... but it seems some really are feeling pressure to get those reviews.

Seashanty, I'm not sure if your comment about not "contacting anyone about it" was directed at me because it wasn't posted as a reply to my comment. Who would you contact about it? TripAdvisor? Feel free. I'm not offering an incentive for TripAdvisor reviews. I specifically said "I discourage guests from leaving TA reviews."
Google reviews boost your SEO, TA reviews do not. You're not feeling pressure to advertise and boost your ranking in Google search results? How much do you pay to list on different websites to increase your online exposure? And what about repeat guests? You don't feel a need to encourage folks to stay again?
I don't feel my actions are shady, but I can understand how some folks might feel I'm walking a fine line. Purchasing 300 positive reviews when you buy a B&B is dishonest. The new owners didn't earn those reviews.
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Purchasing 300 positive reviews when you buy a B&B is dishonest. The new owners didn't earn those reviews.

I'm going to play devil's advocate here for a moment. If you purchase an inn that has a sterling reputation, part of what you're purchasing is that "goodwill." It's actually an asset when valuing the business.
Reviewers don't just comment on the owners. They comment on the rooms. The property. The area. Things to do in the region. The tablecloths. The linens. The beds. Unless you burned the place to the ground and relocated it at closing, I think leaving up previous owner reviews is perfectly acceptable. Newer reviewers will make the comment that the inn has new owners, and they're wonderful, terrible, ugly, etc. Readers understand context. And truthfully, they only read down 3 or 4 reviews at most.
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"They comment on the rooms. The property. The area. Things to do in the region. The tablecloths. The linens. The beds."
Aside from rooms & location, I humbly beg to differ on your assessment. New owners wouldn't necessarily have the same decor, furniture, tablecloths, linens, or beds. (I started from almost nothing. My supposed "turnkey" B&B was a joke!) New owners definitely wouldn't serve the same breakfasts, or greet the guests in the same manner, or provide the same recommendations for local sights and dining. New owners may also have different policies regarding cancellations, deposits, refunds, or even check-in times.
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"They comment on the rooms. The property. The area. Things to do in the region. The tablecloths. The linens. The beds."
Aside from rooms & location, I humbly beg to differ on your assessment. New owners wouldn't necessarily have the same decor, furniture, tablecloths, linens, or beds. (I started from almost nothing. My supposed "turnkey" B&B was a joke!) New owners definitely wouldn't serve the same breakfasts, or greet the guests in the same manner, or provide the same recommendations for local sights and dining. New owners may also have different policies regarding cancellations, deposits, refunds, or even check-in times.

And all of that comes out in the reviews. We lost a good chunk of the PO's repeat guests because they didn't like our policies. We did serve the same breakfasts, we bought their recipes. Everything was the same for several years until we had the vision to change things. We're still changing things and it's been 13 years. We didn't have the money to make changes at first.
After a couple of years the PO reviews were buried.
For us, that was only 10 reviews or so, but we bought a place with a good rep and we weren't going out of our way to make waves.
It's very hard to get TA to change the status quo. We had 3 b&B's that were closed for years but TA would not remove them. They are gone now, but another one that's been closed for years has just started showing up again.
If you change the name of the property TA will eventually catch on.