Did the pizza industry, particularly small mom and pop chains, experience any unusual or notable growth (if any) between the years 1988 to 1996 due to the popularity and televised syndication of the Teenage Mutant Ninja Turtles? What was the industry like as a whole before the show aired?

This is a tricky one to answer, but I'm going to take a stab at it. As individual cases of small mom and pop shops seeing an increase in sales are extremely difficult to come by, I will be focusing on the major players.

By "major players" in the pizza industry, a few in particular come to mind - Pizza Hut, Domino's, and Papa John's.

Papa John's - founded in 1984 - doesn't go public until 1993, the latter half of the time period in your question. At the time of the initial public offering (being June 9th of that year), Papa John's own stock page suggests that the company was $2.25/share. I've seen secondhand accounts that it opened at $13 at share, but I couldn't find anything from 1993 to back this up; nonetheless, by the end of the original Turtles series (being November 2nd, 1996) the stock sold at triple that - the price on November 1st being $8.29 a share.

Is this because of the Ninja Turtles? Hard to say, but I'm going to go with unlikely. Most sources I found on the rise of Papa John's suggest that the main factors going into the company's rise were quality ingredients, acting like an independent pizza shop despite being a chain while keeping consistency, and the cheap price to franchise (often less than $100,000).

Domino's Pizza - founded in 1960 - does not go public until 2004, and I had no luck finding any financial information for the time period questioned. However, company sales were certainly up in the 1990s - an article from the Los Angeles Times states:

Closely held Ann Arbor, Mich.-based Domino's, which was advised in the transaction by J.P. Morgan Securities, had 1997 sales of $3.2 billion, up from $2.8 billion in 1996. The agreement signed Friday was expected to be completed within a few months.

which implies that sales were certainly good. Was this increase in revenue caused by the Ninja Turtles? Once again, probably not. The chain had seen a massive expansion - by 1983, the company had opened a thousand stores and expanded out of the country by 1993 into international branches. The Ninja Turtles could have helped in theory - the chain cameos in the first Ninja Turtles film - but the chain was already experiencing major growth, turtles or not.

Pizza Hut - founded in 1958 - had already been bought by PepsiCo in 1977, but I couldn't find stock prices from that specific year. On the day of the debut of the TMNT cartoon, however - December 14th, 1987 - PepsiCo stock was $5.35 a share; by the end of the series, it was more than five times that - closing out at an even $30 a share. Of course, this is PepsiCo as a whole - that stock price was accounting for earnings from the soda industry, the pizza industry, the snack industry, the introduction of Pepsi plants and Pizza Huts in the opening Soviet Union, etc. Even so, I will argue that Pizza Hut - and therefore PepsiCo - was somewhat aided by the Ninja Turtles.

After the success of the first Ninja Turtles movie, the characters went on a live show tour. Who funded it? Pizza Hut. As an article from the Chicago Tribune states:

Pizza Hut has pumped more than $20 million into the new Teenage Mutant Ninja Turtle album it is offering in its restaurants-more than 2 million already have been sold-along with its 40-city live rock concert/theatrical production, ''Coming Out of Their Shells,'' which will be at the Arie Crown Theatre for 10 performances Tuesday through next Sunday.

And this was on top of a marketing campaign between the two parties; unlike with earlier cameos in Back to the Future, however, Pizza Hut doesn't appear in any of the 90s Turtles movies. This doesn't deter them, however, as they appear in the Ninja Turtles II arcade game and, as shown in the first commercial I linked, gave coupons with the VHS release of the film. On top of that (and it has been a lot), the soundtrack was given away with every pan pizza ordered at the chain.

As MTV noted in their coverage of the brand alliance:

"Over 2 million cassette tapes of the show’s soundtrack were sold that year with the purchase of a personal pan pizza at Pizza Hut. The official Turtles Tour video made no attempt to hide that Pizza Hut was the real captain behind the wheel. Even Senior Vice President of Marketing for Pizza Hut, David Novack, appeared midway through to deliver a press statement on Pizza Hut's behalf: 'We're just absolutely thrilled to get the world's most famous pizza eaters to hook up with the number one pizza company in the world. Pizza Hut will launch the most aggressive promotion ever done in the record industry to support the Turtles' new music, which I'm sure all of America will love.'"

In conclusion, while I wouldn't call it a major player in the pizza industry beyond their connections to one of the largest chains, the Teenage Mutant Ninja Turtles during their commercial peak certainly left their mark on the pizza industry.